FIRST AMENDMENT TO AGREEMENT RELATING TO RETENTION AND NONCOMPETITION AND OTHERCOVENANTS

Exhibit 10.31

FIRST AMENDMENT TO AGREEMENT RELATING TO RETENTION AND

NONCOMPETITION AND OTHER COVENANTS

First Amendment (the “First Amendment”), dated as of April 1, 2011 (the “Effective Date”), to Agreement Relating to Retention and Noncompetition and Other Covenants by and between Lazard Group LLC, a Delaware limited liability company, and successor to Lazard LLC (“Lazard”), on its behalf and on behalf of its subsidiaries and affiliates (collectively with Lazard, and its and their predecessors and successors, the “Firm”), and Matthieu Bucaille (formerly known as the “Working Partner” and from and after the date hereof as the “Executive”), dated as of October 4, 2004 (the “Agreement”); and

WHEREAS, the Firm and the Executive wish to amend the Agreement to (i) make Lazard Ltd, a company incorporated under the laws of Bermuda (“PubliCo”), a party to the Agreement, as amended by the First Amendment, through PubliCo’s execution of the First Amendment, and (ii) modify Schedule I to such Agreement to, among other things, reflect the Executive’s appointment as Chief Financial Officer of Lazard and PubliCo and to revise certain terms of the Agreement in order to be consistent with agreements with other executive officers of Lazard and PubliCo.

NOW, THEREFORE, in consideration of the premises contained herein and for other good and valuable consideration, the receipt and adequacy of which are hereby acknowledged, the Executive, Lazard and PubliCo hereby agree as follows:

Effective as of the Effective Date, PubliCo shall become a party to the Agreement and Schedule I of the Agreement shall hereby be amended and restated in the form attached hereto.

IN WITNESS WHEREOF, the Executive and the Board of Directors of each of Lazard and PubliCo have caused this First Amendment to be executed and delivered on the date first above written.

April 1, 2011

SCHEDULE I

Effective upon the effective date of the First Amendment to this Agreement (the “First Amendment Effective Date”), this Schedule I shall take effect and its provisions shall constitute binding and enforceable agreements of the Firm.

1. Title. Notwithstanding anything to the contrary contained in Section 3(b) of this Agreement, from the First Amendment Effective Date through March 23, 2013, the Executive shall serve as Chief Financial Officer of Lazard Group LLC and PubliCo.

2. Compensation. Notwithstanding anything to the contrary contained in Sections 3(c)(i) and (ii) of this Agreement, subject to the Executive’s continued employment with the Firm during the period from the First Amendment Effective Date through March 23, 2013, the Executive shall be entitled to receive (i) an annual base salary of not less than $750,000 (“Base Salary”) and (ii) so long as the Executive remains employed by the Firm through the end of the applicable fiscal year of Lazard, an annual bonus to be determined under the terms of the applicable annual bonus plan of Lazard on the same basis as annual bonus is determined for other executive officers of PubliCo, with such bonus to be paid in the same ratio of cash to equity awards as is applicable to executives of the Firm receiving bonuses at a level comparable to the bonus of the Executive. For purposes hereof, the term Base Salary shall refer to Base Salary as in effect from time to time, including any increases. Notwithstanding anything to the contrary contained in Section 3(c)(iv) of this Agreement, during the portion of the Term commencing on the First Amendment Effective Date, subject to the Executive’s continued employment, the Executive shall be eligible to participate in the employee retirement and welfare benefit plans and programs of the type made available to the senior most executives of the Firm generally, in accordance with their terms and as such plans and programs may be in effect from time to time, including, without limitation, savings, profit-sharing and other retirement plans or programs, 401(k), medical, dental, flexible spending account, hospitalization, short-term and long-term disability and life insurance plans. Furthermore, during the portion of the Term commencing on the First Amendment Effective Date and ending on March 23, 2013, subject to the Executive’s continued employment, the Executive shall be entitled to reimbursement (A) in an amount not to exceed $10,000 per month, for the rent on the Executive’s residence in the New York City metropolitan area (the “Housing Allowance”) and (B) for private school tuition for each of the Executive’s children who is under the age of 18 years old (the “Tuition Reimbursement”). Within 30 days following the end of each calendar quarter, the Executive will provide the Firm with an invoice that sets forth the amount, if any, incurred with respect to the Housing Allowance and the Tuition Reimbursement during the preceding calendar quarter. Within 30 days following the Firm’s receipt of each such invoice, the Firm shall pay the Executive an amount in cash in U.S. dollars equal to the amount set forth on the invoice, provided that, with respect to the Housing Allowance, the amount of such payment and any previously reimbursed payments shall not exceed the maximum amount set forth in this

paragraph 2. Any amount reimbursed to the Executive with respect to each of the Housing Allowance and the Tuition Reimbursement in any given calendar year shall not affect the amount reimbursed in any other calendar year, and the Executive’s right to reimbursement with respect to each of the Housing Allowance and the Tuition Reimbursement may not be liquidated or exchanged for any other benefit.

3. Severance Pay and Benefits under Certain Circumstances. Notwithstanding anything to the contrary contained in Section 3(d) of this Agreement, in the event that during the period commencing on the First Amendment Effective Date and concluding on March 23, 2013, the Executive’s employment with the Firm is terminated by the Firm without Cause or by the Executive for Good Reason (in each case, as defined below) (a “Qualifying Termination”), Lazard shall pay the Executive, in a lump sum in cash within thirty (30) days after the Date of Termination, the aggregate of the following amounts: (i) any unpaid Base Salary through the Date of Termination; (ii) any earned and unpaid cash bonus amounts for fiscal years of Lazard completed prior to the Date of Termination (determined in accordance with paragraph 2 above and with any such bonus to be paid in full in cash); and (iii) the product of (1) the “Severance Multiple” (as defined below) and (2) the sum of (x) the Base Salary and (y) the average annual bonus (or, to the extent applicable, cash distributions, and including any bonuses paid in the form of equity awards based on the grant date value of such equity awards in accordance with the normal valuation methodology used by Lazard) paid or payable to the Executive for the two completed fiscal years of Lazard immediately preceding the fiscal year during which occurs the Date of Termination (the “Average Bonus”). In addition, (i) for a period of months equal to the product of (1) 12 and (2) the Severance Multiple, the Executive and his eligible dependents shall continue to be eligible to participate in the medical and dental benefit plans of Lazard on the same basis as the Executive participated in such plans immediately prior to the Date of Termination, to the extent that the applicable plan permits such continued participation for all or any portion of such period (it being agreed that Lazard will use its reasonable efforts to cause such continued coverage to be permitted under the applicable plan for the entire period), which benefits continuation period shall not run concurrently with or reduce the Executive’s right to continued coverage under COBRA and (ii) to the extent permitted under the applicable plan, the Executive will receive additional years of age and service credit equal to the Severance Multiple for purposes of determining his eligibility for and right to commence receiving benefits under the retiree health care benefit plans of Lazard Group. For purposes of the provision of the health care benefits as provided above, the amount of such health care benefits provided in any given calendar year shall not affect the amount of such benefits provided in any other calendar year, and the Executive’s right to the health care benefits may not be liquidated or exchanged for any other benefit.

In addition, in the case of a Qualifying Termination, with respect to the fiscal year of Lazard during which the Date of Termination occurs, the Executive shall receive a pro-rata annual bonus payable in cash determined as follows:

(i) if (A) the Date of Termination occurs prior to or on March 23, 2013 and (B) with respect to the fiscal year during which the Date of Termination occurs, (1) the Executive was reasonably expected by Lazard to be a “covered employee” (within the meaning of Section 162(m) of the Internal Revenue Code of 1986, as amended (the “Code”)) prior to his Date of Termination, and (2) the annual bonus that the Executive was eligible to receive for such

year was originally intended by Lazard to satisfy the performance-based exception under Section 162(m) of the Code (without regard to any entitlement to payment upon termination of employment), the Executive’s pro-rata annual bonus shall equal the product of (1) the amount determined by the Compensation Committee based on the Firm’s actual performance for the fiscal year of the Firm in which the Date of Termination occurs on the same basis as annual bonus is determined for other executive officers of the Firm (which, subject to the limits on any such bonus due to the level of satisfaction of the performance goals previously established for purposes of Section 162(m) of the Code, shall not represent (on an annualized basis) a percentage of the Executive’s bonus for the fiscal year preceding the fiscal year in which the Date of Termination occurs that is lower than the average corresponding percentage applicable to active executives of Lazard who received bonuses for such prior fiscal year in amounts within 5% of the Executive’s bonus for such prior fiscal year), and (2) a fraction, the numerator of which is the number of days elapsed in the fiscal year of Lazard in which occurs the Date of Termination through the Date of Termination, and the denominator of which is 365 (the “Pro-Ration Fraction”); or

(ii) if (A) the Date of Termination occurs prior to or on March 23, 2013 and (B) with respect to the fiscal year during which the Date of Termination occurs, the Executive is not reasonably expected by Lazard to be a “covered employee” (within the meaning of Section 162(m) of the Code) prior to his Date of Termination, the pro-rata annual bonus shall equal the product of (1) the Average Bonus and (2) the Pro-Ration Fraction.

The pro-rata annual bonus determined pursuant to clause (i) or (ii) above, as applicable, shall be paid at such time or times as Lazard otherwise makes incentive payments for such fiscal year (and in all events prior to March 15 of the year following the year in which the Date of Termination occurs).

For all purposes of this Agreement, including without limitation, Sections 2(g)(ii) and Section 5(a), a resignation on or prior to March 23, 2013 by the Executive for Good Reason shall be treated as a termination of the Executive by the Firm without Cause.

In no event shall the Executive be obligated to seek other employment or take any other action by way of mitigation of the amounts payable to the Executive under any of the provisions of this paragraph 3 of this Schedule and such amounts shall not be reduced whether or not the Executive obtains other employment. Except as provided in Section 16(f) of this Agreement, the Firm’s obligation to make the payments provided for in this Agreement and otherwise to perform its obligations hereunder shall not be affected by any set-off, counterclaim, recoupment, defense or other claim, right or action which the Firm may have against the Executive.

4. Certain Definitions. For purposes of the Agreement and this Schedule I, as applicable, the following terms shall have the following meanings:

Notwithstanding the definition of “Date of Termination” set forth in Section 5 of the Agreement, for purposes of the Agreement, including Section 5, and this Schedule I, “Date of Termination” shall mean (i) if the Executive’s employment is terminated by the Firm for Cause, the date of receipt of the notice of termination from the Firm or any later date specified therein within 30 days of such notice, as the case may be, (ii) if the Executive’s

employment is terminated by the Firm other than for Cause or Disability, the date on which the Firm notifies the Executive of such termination, (iii) if the Executive’s employment is voluntarily terminated by the Executive without Good Reason, the date as specified by the Executive in the Notice of Termination, which date shall not be less than three months after the Executive notifies the Firm of such termination, unless waived in writing by the Firm, (iv) if the Executive’s employment is terminated by the Executive for Good Reason, the earlier of (A) the last day of the cure period (assuming no cure has occurred) and (B) the date Lazard formally notifies the Executive that it does not intend to cure, unless Lazard and the Executive agree to a later date, which shall in no event be later than 30 days following the first to occur of the dates set forth in clauses (A) and (B) of this clause (iv), and (v) if the Executive’s employment is terminated by reason of death or Disability, the Date of Termination shall be the date of death of the Executive or the date on which the Executive’s employment due to Disability is effective for purposes of the applicable long-term disability plan of the Firm. The Firm and the Executive shall take all steps necessary (including with regard to any post-termination services by the Executive) to ensure that any termination of the Executive’s employment described in the Agreement, including Schedule I, constitutes a “separation from service” within the meaning of Section 409A of the Code, and notwithstanding anything contained herein to the contrary, the date on which such separation from service takes place shall be the “Date of Termination.”

Notwithstanding the definition of “Cause” set forth in Section 2(g)(iv) of the Agreement, from and after the First Amendment Effective Date, for all purposes of this Agreement, including Section 2(g)(iv) and this Schedule I, “Cause” shall mean: (A) conviction of the Executive of, or a guilty or nolo contendere plea (or the equivalent in a non-United States jurisdiction) by the Executive to, a felony (or the equivalent in a non-United States jurisdiction), or of any other crime that legally prohibits the Executive from working for the Firm; (B) breach by the Executive of a regulatory rule that materially adversely affects the Executive’s ability to perform his duties to the Firm; (C) willful and deliberate failure on the part of the Executive (i) to perform his employment duties in any material respect or (ii) to follow specific reasonable directions received from the Firm, in each case following written notice to the Executive of such failure and, if such failure is curable, the Executive’s failing to cure such failure within a reasonable time (but in no event less than 30 days); or (D) a breach of the Covenants that is (individually or combined with other such breaches) demonstrably and materially injurious to Lazard or any of its affiliates. Notwithstanding the foregoing, with respect to the events described in clauses (B) and (C)(i) hereof, the Executive’s acts or failure to act shall not constitute Cause to the extent taken (or not taken) based upon the direct instructions of the Board of Directors of PubliCo.

“Good Reason” shall mean (i) the assignment to the Executive of any duties inconsistent in any material respect with the Executive’s position (including status, offices, titles and reporting requirements), authority, duties or responsibilities as in effect as of the First Amendment Effective Date, or any other action by the Firm which results in a material diminution in such position, authority, duties or responsibilities from the level in effect as of the First Amendment Effective Date, (ii) a material breach by the Firm of the terms of this Agreement, including, without limitation, any material failure by the Firm to comply with paragraph 2 of this Schedule, or (iii) any requirement that the Executive’s principal place of employment be relocated to a location that increases the Executive’s commute from his primary residence by more than 30 miles. In the event of a termination for Good Reason, the notice

requirements of Section 1 shall not apply. Notwithstanding the foregoing, a termination for Good Reason shall not have occurred unless (i) the Executive gives written notice to Lazard of termination of employment within ninety (90) days after the Executive first becomes aware of the occurrence of the circumstances constituting Good Reason, specifying in reasonable detail the circumstances constituting Good Reason, and Lazard has failed within thirty (30) days after receipt of such notice to cure the circumstances constituting Good Reason, and (ii) the Executive’s “separation from service” (within the meaning of Section 409A of the Code) occurs no later than two years following the initial existence of one or more of the circumstances giving rise to Good Reason.

“Severance Multiple” shall equal (i) two (2), if the Date of Termination occurs prior to a Change of Control or (ii) three (3), if the Date of Termination occurs on or following the date of a Change of Control.

5. Excise Tax. In the event it shall be determined that any payment, benefit, or distribution by the Firm to or for the benefit of the Executive (whether paid or payable or distributed or distributable pursuant to the terms of this Agreement or otherwise, but determined without regard to any additional payments required under this paragraph) (a “Payment”) would be subject to the excise tax imposed by Section 4999 of the Code or any interest or penalties are incurred by the Executive with respect to such excise tax (such excise tax, together with any such interest and penalties, are hereinafter collectively referred to as the “Excise Tax”), then the Executive shall be entitled to receive an additional payment (a “Gross-Up Payment”) in an amount such that after payment by the Executive of all taxes (including any interest or penalties imposed with respect to such taxes), including, without limitation, any income taxes (and any interest and penalties imposed with respect thereto) and Excise Tax imposed upon the Gross-Up Payment, but excluding any income taxes and penalties imposed pursuant to Section 409A of the Code, the Executive retains an amount of the Gross-Up Payment equal to the Excise Tax imposed upon the Payments.

The Firm’s obligation to make Gross-Up Payments under this paragraph 5 shall not be conditioned upon the Executive’s termination of employment. All determinations required to be made under this paragraph, including whether and when a Gross-Up Payment is required and the amount of such Gross-Up Payment and the assumptions to be utilized in arriving at such determination, shall be made by Deloitte & Touche LLP or such other certified public accounting firm reasonably acceptable to the Firm as may be designated by the Executive (the “Accounting Firm”), which shall provide detailed supporting calculations both to Lazard and the Executive within fifteen (15) business days of the receipt of notice from the Executive that there has been a Payment, or such earlier time as is requested by Lazard. All fees and expenses of the Accounting Firm shall be borne solely by the Firm. Any Gross-Up Payment shall be paid by the Firm to the Executive within five days of the later of (i) the due date for the payment of any Excise Tax, and (ii) the receipt of the Accounting Firm’s determination. Any determination by the Accounting Firm shall be binding upon the Firm and the Executive. As a result of the uncertainty in the application of Section 4999 of the Code at the time of the initial determination by the Accounting Firm hereunder, it is possible that Gross-Up Payments which will not have been made by the Firm should have been made (“Underpayment”) or that Gross-Up Payments which were made by the Firm should not have been made (“Overpayment”). In the event that there occurs an Underpayment and the Executive thereafter is required to make a

payment of any Excise Tax, the Accounting Firm shall determine the amount of the Underpayment that has occurred and any such Underpayment shall be promptly paid by the Firm to or for the benefit of the Executive. In the event that there occurs an Overpayment and the Executive becomes entitled to receive any refund with respect to the Excise Tax, the Executive shall promptly pay to the Firm the amount of such refund (together with any interest paid or credited thereon after taxes applicable thereto).

Any Gross-Up Payment, as determined pursuant to this paragraph 5, shall be paid by the Firm to the Executive within five (5) days of the receipt of the Accounting Firm’s determination; provided that, the Gross-Up Payment shall in all events be paid no later than the end of the Executive’s taxable year next following the Executive’s taxable year in which the Excise Tax (and any income or other related taxes or interest or penalties thereon) on a Payment is remitted to the Internal Revenue Service or any other applicable taxing authority or, in the case of amounts relating to a claim from the Internal Revenue Service or another tax authority that does not result in the remittance of any federal, state, local and foreign income, excise, social security and other taxes, the calendar year in which the claim is finally settled or otherwise resolved. Notwithstanding any other provision of this paragraph 5, the Firm may, in its sole discretion, withhold and pay over to the Internal Revenue Service or any other applicable taxing authority, for the benefit of the Executive, all or any portion of any Gross-Up Payment, and the Executive hereby consents to such withholding.

6. Section 409A. It is the intention of the parties that the payments and benefits to which the Executive could become entitled in connection with termination of employment under this Agreement comply with or are exempt from the definition of “nonqualified deferred compensation” under Section 409A of the Code. In this regard, notwithstanding anything in this Agreement to the contrary, all cash amounts that become payable under Section 3 of this Schedule I on account of the Executive’s termination of employment shall be paid no later than March 15 of the year following the year in which the Date of Termination occurs. In the event the parties determine that the terms of this Agreement, including this Schedule I, do not comply with Section 409A, they will negotiate reasonably and in good faith to amend the terms of this Agreement and/or Schedule I such that they comply (in a manner that attempts to minimize the economic impact of such amendment on the Executive and the Firm) within the time period permitted by the applicable Treasury Regulations. During the portion of the Term commencing on the First Amendment Effective Date and ending on March 23, 2013, subject to the Executive’s continued employment, the Executive shall be entitled to an additional payment (an “Additional Payment”) with respect to both the Housing Allowance and the Tuition Reimbursement, in an amount such that after payment by the Executive of all taxes (including any interest or penalties imposed with respect to such taxes), including, without limitation, any income taxes (and any interest and penalties imposed with respect thereto) upon the Additional Payment, but excluding any income taxes and penalties imposed pursuant to Section 409A of the Code, the Executive retains an amount of the Additional Payment equal to all taxes upon the Housing Allowance and the Tuition Reimbursement (such taxes, the “Additional Taxes”). The Additional Payment shall in all events be paid no later than the end of the Executive’s taxable year next following the Executive’s taxable year in which the relevant Additional Taxes (and any income or other related taxes or interest or penalties thereon) on the Housing Allowance or the Tuition Reimbursement, as applicable, is remitted to the Internal

Revenue Service or any other applicable taxing authority or, in the case of amounts relating to a claim from the Internal Revenue Service or another tax authority that does not result in the remittance of any federal, state, local and foreign income, excise, social security and other taxes, the calendar year in which the claim is finally settled or otherwise resolved. Notwithstanding any other provision of this paragraph 6, the Firm may, in its sole discretion, withhold and pay over to the Internal Revenue Service or any other applicable taxing authority, for the benefit of the Executive, all or any portion of any Additional Payment, and the Executive hereby consents to such withholding.

7. Miscellaneous.

Your HoldCo Interests (as per Section 2(b)) are 0.4756 and your Profit Interests (as per Section 2(d)) are 0.4756.

Section 5(a). Section 5(a) of the Agreement is hereby amended and restated in its entirety to read as follows: The Executive acknowledges and recognizes the highly competitive nature of the businesses of the Firm. The Executive further acknowledges and agrees that in connection with the Reorganization, and in the course of the Executive’s subsequent employment with the Firm, the Executive has been and shall be provided with access to sensitive and proprietary information about the clients, prospective clients, knowledge capital and business practices of the Firm, and has been and shall be provided with the opportunity to develop relationships with clients, prospective clients, consultants, employees, representatives and other agents of the Firm, and the Executive further acknowledges that such proprietary information and relationships are extremely valuable assets in which the Firm has invested and shall continue to invest substantial time, effort and expense. As an Associe-Gerant and Class A Member of Lazard, the Executive is currently bound by certain restrictive covenants, including a noncompetition restriction, pursuant to the terms of the Goodwill Agreement. Accordingly, the Executive hereby reaffirms and agrees that while employed by the Firm and thereafter until (i) three months after the Executive’s date of termination of employment for any reason other than a termination by the Firm without Cause or (ii) one month after the date of the Executive’s termination by the Firm without Cause (such period, in either case, the “Noncompete Restriction Period”), the Executive shall not, directly or indirectly, on the Executive’s behalf or on behalf of any other person, firm, corporation, association or other entity, as an employee, director, advisor, partner, consultant or otherwise, engage in a “Competing Activity,” or acquire or maintain any ownership interest in, a “Competitive Enterprise.” For purposes of this Agreement, (i) “Competing Activity” means the providing of services or performance of activities for a Competitive Enterprise in a line of business that is similar to any line of business to which the Executive provided services to the Firm in a capacity that is similar to the capacity in which the Executive acted for the Firm while employed by the Firm, and (ii) “Competitive Enterprise” shall mean a business (or business unit) that (A) engages in any activity or (B) owns or controls a significant interest in any entity that engages in any activity, that in either case, competes anywhere with any activity in which the Firm is engaged up to and including the Executive’s Date of Termination. Further, notwithstanding anything in this Section 5, the Executive shall not be considered to be in violation of this Section 5 solely by reason of owning, directly or indirectly, any stock or other securities of a Competitive Enterprise (or comparable interest, including a voting or profit participation interest, in any such Competitive Enterprise) if the Executive’s interest does not exceed 5% of the outstanding capital stock of such Competitive

Enterprise (or comparable interest, including a voting or profit participation interest, in such Competitive Enterprise).

Section 6. Section 6 of the Agreement is hereby amended to replace the definition of “Client” with the following definition: “Client” means any client or prospective client of the Firm, whether or not the Firm has been engaged by such Client pursuant to a written agreement; provided that an entity which is not a client of the Firm shall be considered a “prospective client” for purposes of this sentence only if the Firm made a presentation or written proposal to such entity during the 12-month period preceding the Date of Termination or was preparing to make such a presentation or proposal at the time of the Date of Termination.

Section 12. Section 12 of this Agreement is hereby amended to replace all references to the New York Stock Exchange, Inc.” and the “NYSE” with references to the “Financial Industry Regulatory Authority” and “FINRA”, as applicable.

Section 16(b). Paragraphs 2, 3, 4, 5 and 6 of this Schedule I are hereby added to the list of Sections in Section 16(b) of this Agreement.

Section 16(f). Section 16(f) of this Agreement is hereby amended to add the following words at the end thereof: “except to the extent such withholding or offset is not permitted under Section 409A of the Code without the imposition of additional taxes or penalties on the Executive.”