NEUBERGER BERMAN INC. Liquid Yield OptionTM Notes

Exhibit 4.1

NEUBERGER BERMAN INC.

Liquid Yield Option^TM Notes

due 2021

(Zero Coupon-Senior)

THIRD SUPPLEMENTAL INDENTURE TO

INDENTURE DATED AS OF MAY 4, 2001

Dated as of October 31, 2003

THE BANK OF NEW YORK

as Trustee

^TM Trademark of Merrill Lynch & Co., Inc.

THIRD SUPPLEMENTAL INDENTURE, dated as of October 31, 2003 (this “Third Supplemental Indenture”), among LEHMAN BROTHERS HOLDINGS INC., a Delaware corporation (“Lehman Brothers”), RUBY ACQUISITION COMPANY (to be renamed Neuberger Berman Inc.), a Delaware corporation and a direct wholly owned subsidiary of Lehman Brothers (“Merger Sub”), NEUBERGER BERMAN INC., a Delaware corporation (the “Old Neuberger”), and THE BANK OF NEW YORK, a New York banking corporation, as trustee (the “Trustee”).

RECITALS

WHEREAS, Old Neuberger and the Trustee executed and delivered an Indenture, dated as of May 4, 2001, as amended by the First Supplemental Indenture, dated as of May 2, 2002, and as further amended by the Second Supplemental Indenture, dated as of November 1, 2002 (together, the “Original Indenture,” and, as amended by this Third Supplemental Indenture, collectively, the “Indenture”), to provide for the issuance and delivery by Old Neuberger of its Liquid Yield Option (TM) Notes due 2021 (Zero Coupon-Senior) (the “Securities”);

WHEREAS, Lehman Brothers, Old Neuberger and Merger Sub have entered into an Agreement and Plan of Merger, dated as of July 21, 2003, as amended by the First Amendment to Agreement and Plan of Merger, dated as of September 22, 2003 (as amended, the “Merger Agreement”), pursuant to which Old Neuberger will be merged with and into Merger Sub (the “Merger”), with Merger Sub surviving as a direct wholly owned subsidiary of Lehman Brothers and renamed “Neuberger Berman Inc.”;

WHEREAS, Section 9.01 of the Original Indenture provides that Old Neuberger and the Trustee may amend the Original Indenture or the Securities without the consent of any Securityholder to comply with Article 5 and Section 11.14 thereof;

WHEREAS, Merger Sub and Lehman Brothers desire to enter into this Third Supplemental Indenture and to provide that, effective as of the effective time of the Merger (the “Effective Time”), Merger Sub will expressly assume all of the obligations of Old Neuberger under the Indenture and to provide that upon a Holder’s conversion of a Security in accordance with the terms of the Indenture, the Holder will receive the kind and amount of securities and cash which such Holder would have received immediately after the Merger if such Holder had converted the Security immediately before the Effective Time; and

WHEREAS, all things necessary for the execution of this Third Supplemental Indenture, and to make this Third Supplemental Indenture a valid supplement to the Original Indenture according to its terms and a valid and binding agreement of Merger Sub and Lehman Brothers, have been done.

NOW, THEREFORE, in consideration of the mutual agreements contained herein and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto agree as follows for the benefit of each other and for the equal and ratable benefit of the Holders of the Securities:

ARTICLE I

RATIFICATION; DEFINITIONS

Section 1.1. Third Supplemental Indenture. This Third Supplemental Indenture constitutes an integral part of, is supplemental to, and is entered into in accordance with, Section 9.01 of the Original Indenture and, except as modified, amended and supplemented by this Third Supplemental Indenture, the provisions of the Original Indenture are ratified and confirmed in all respects and shall remain in full force and effect.

Section 1.2. Definitions. For all purposes of this Third Supplemental Indenture:

(a) Capitalized terms used herein without definition shall have the meanings specified in the Original Indenture; and

(b) The terms “herein,” “hereof,” “hereunder” and other words of similar import refer to this Third Supplemental Indenture.

ARTICLE II

AMENDMENTS TO THE ORIGINAL INDENTURE

Section 2.1. Assumption of Obligations by Merger Sub. Merger Sub hereby expressly assumes all of the obligations of Old Neuberger under the Securities and the Indenture, including, without limitation, (i) the due and punctual payment of the principal and Accrued Original Discount of, premium, if any, and interest on all of the Securities, as applicable, and (ii) the performance and observance of every covenant of the Indenture on the part of Old Neuberger to be performed or observed.

Section 2.2. Amendment to the First Paragraph. The first paragraph of the Original Indenture is hereby amended so that the term “the Company” as used therein shall mean Merger Sub; provided that references to the term “the Company” as it relates solely to the Common Stock or the issuance of the Common Stock shall mean Lehman Brothers. Pursuant to Section 5.01 of the Original Indenture, Merger Sub shall succeed to, and be substituted for, and may exercise every right and power of, Old Neuberger under the Original Indenture with the same effect as if Merger Sub had been named as “the Company” therein; and, except as otherwise provided for in the Original Indenture, Old Neuberger shall be discharged from all obligations and covenants under the Original Indenture and the Securities.

Section 2.3. Amendments to Section 1.01.

(a) Section 1.01 of the Original Indenture is hereby amended so that the term “Common Stock” shall mean the shares of common stock, $0.10 par value per share, of Lehman Brothers as it exists on the date of this Indenture or any other shares of Capital Stock of Lehman Brothers into which the Common Stock shall be reclassified or changed.”

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(b) Section 1.01 of the Original Indenture is hereby amended so that the terms “Effective Time,” “Lehman Brothers,” “Merger,” “Merger Agreement” and “Merger Sub” shall have the meanings therein given them in this Third Supplemental Indenture.

(c) Section 1.01 of the Original Indenture is hereby amended to include the following new definitions:

“Conversion Ratio” shall mean the sum of the Exchange Ratio plus the Special Exchange Ratio.

“Exchange Ratio” shall mean 0.4741, subject to adjustment pursuant to Sections 11.06, 11.07, 11.08, 11.12 and 11.14.

“Merger Consideration” shall mean a unit consisting of $9.49 in cash, without interest, and a fraction of a share of common stock, par value $0.10 per share, of Lehman Brothers equal to the Exchange Ratio, and in the Securities and this Indenture may be expressed as one or more unit(s) of Merger Consideration.

“Special Exchange Ratio” shall mean 0.1363, subject to adjustment pursuant to Sections 11.06, 11.07, 11.08, 11.12 and 11.14.

Section 2.4. Adjusted Conversion Rights. Pursuant to Section 11.14 of the Original Indenture, and subject to the terms and conditions of the Securities and the Indenture, the Holder of a Security outstanding on the Effective Time may convert it at any time during the period stated in paragraph 8 of the Securities for 13.8879 units of the Merger Consideration per $1,000 Principal Amount at Maturity thereof. The Securities and Article 11 of the Original Indenture are hereby deemed amended accordingly.

Section 2.5. Adjustments to Exchange Ratio and Special Exchange Ratio. The Conversion Rate shall not be subject to further adjustment pursuant to Sections 11.06, 11.07, 11.08, 11.12 and 11.14 of the Original Indenture. Each of the Exchange Ratio and the Special Exchange Ratio shall be subject to adjustments that are as nearly equivalent as may be practicable to the adjustments provided for in such Sections. The Securities and Sections 11.06, 11.07, 11.08, 11.12 and 11.14 of the Original Indenture are hereby deemed amended accordingly.

Section 2.6. Amendment to Section 12.02. The first subparagraph of Section 12.02 of the Original Indenture is hereby amended by replacing it in its entirety with the following:

“if to the Company:

Neuberger Berman Inc.

605 Third Avenue

New York, New York 10158

Telephone No. (212) 476-9000

Facsimile No. (212) 746-9862

Attention: General Counsel

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and

Lehman Brothers Holdings Inc.

745 Seventh Avenue

New York, New York 10019

Telephone No. (212) 526-7000

Facsimile No. (212) 526-0339

Attention: Corporate Law Department”

ARTICLE III

AMENDMENTS TO CERTAIN PROVISIONS OF THE SECURITIES;

NOTATION ON THE SECURITIES

Section 3.1. Amendments to Paragraph 8(a) of the Securities. Paragraph 8(a) of the Securities is hereby amended by replacing it in the entirety with the following:

“(a) CONVERSION BASED ON COMMON STOCK PRICE. Subject to the provisions of this paragraph 8 and notwithstanding the fact that any condition to conversion in paragraph 8(b), 8(c) or 8(d) has not been satisfied, Holders may convert the Securities into 13.8879 units of the Merger Consideration per $1,000 Principal Amount at Maturity on a Conversion Date in any calendar quarter commencing after June 30, 2001, if, as of the last day of the preceding calendar quarter, the Sale Price of the Common Stock for at least 20 trading days in a period of 30 consecutive trading days ending on the last trading day of such preceding calendar quarter is greater than the conversion trigger price for the calendar quarter in which such Conversion Date falls. The “conversion trigger price” for any calendar quarter shall be a reference percentage, beginning at 120%, and declining ..12658% per quarter thereafter until it reaches 110.00018% for the quarter beginning April 1, 2021, of the accreted conversion price per share of Common Stock on the last day of such preceding calendar quarter.

The “accreted conversion price” per share of Common Stock as of any day equals the quotient of:

For illustrative purposes only, the table below shows the conversion trigger price per share of Common Stock in respect of each of the first 16 calendar quarters commencing with the

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execution of the Third Supplemental Indenture hereto, dated as of October 31, 2003. The conversion trigger price for any calendar quarter starting with the fourth calendar quarter in 2003 shall be the conversion trigger price as of the last day of the immediately preceding calendar quarter as set forth in the table below. These conversion trigger prices reflect the accreted conversion price per share of Common Stock multiplied by the applicable percentage for the respective calendar quarter. Thereafter, the accreted conversion price per share of Common Stock increases each calendar quarter by the accreted Original Issue Discount for the quarter and the applicable percentage declines by 0.12658% per quarter. The conversion trigger price for the calendar quarter beginning April 1, 2021 is $129.67.

* This table assumes no events have occurred that would require an adjustment to the conversion rate.”

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Section 3.2. Amendment to Paragraph 8(d) of the Securities. The fourth paragraph set forth within Paragraph 8(d) of the Securities is hereby amended by replacing it in the entirety with the following:

“The Conversion Rate is 13.8879 units of the Merger Consideration per $1,000 Principal Amount at Maturity. The Exchange Ratio portion of the Merger Consideration is subject to adjustment in certain events described in the Indenture. The Company will deliver cash or a check in lieu of any fractional share of Common Stock.”

Section 3.3. Notation on Securities.

(a) The Securities, as amended by the provisions of this Third Supplemental Indenture, shall bear a notation substantially to the following effect:

“THE TERMS OF THIS SECURITY HAVE BEEN AMENDED TO THE EXTENT PROVIDED IN THE THIRD SUPPLEMENTAL INDENTURE, DATED AS OF OCTOBER 31, 2003, BETWEEN THE COMPANY, LEHMAN BROTHERS HOLDINGS INC. (“LEHMAN BROTHERS”) AND THE TRUSTEE. THE THIRD SUPPLEMENTAL INDENTURE WAS ENTERED INTO BETWEEN THE COMPANY, LEHMAN BROTHERS AND THE TRUSTEE PURSUANT TO SECTION 9.01 OF THE INDENTURE TO COMPLY WITH ARTICLE 5 AND SECTION 11.14 THEREOF. THE TERMS OF THIS SECURITY INCLUDE THOSE STATED IN THE INDENTURE, AS SUPPLEMENTED BY THE THIRD SUPPLEMENTAL INDENTURE, AND HOLDERS ARE REFERRED TO THE INDENTURE AND THE THIRD SUPPLEMENTAL INDENTURE FOR A STATEMENT OF THOSE TERMS.”

(b) The Trustee hereby agrees to cause the Securities to bear the above notation pursuant to, and upon satisfaction of, the conditions set forth in Sections 9.05, 9.06, 12.04 and 12.05 of the Original Indenture.

Section 3.4. Conversion following Effective Time. As contemplated in the notice sent to Securityholders by Old Neuberger on October 16, 2003 pursuant to Section 11.13 of the Original Indenture and paragraph 8(d) of the Securities, Lehman Brothers and Merger Sub acknowledge that the Securities may be surrendered for conversion at any time from the Effective Time of the Merger until 15 days after the Effective Time into 13.8879 units of the Merger Consideration per $1,000 Principal Amount at Maturity thereof.

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ARTICLE IV

MISCELLANEOUS

Section 4.1. Effectiveness. This Third Supplemental Indenture shall become effective upon the Effective Time.

Section 4.2. Trust Indenture Act Controls. If any provision of this Third Supplemental Indenture limits, qualifies or conflicts with another provision which is required to be included in this Third Supplemental Indenture by the TIA, the required provision shall control.

Section 4.3. Incorporation into Indenture. The Third Supplemental Indenture and all its provisions shall be deemed a part of the Original Indenture in the manner and to the extent herein and therein provided.

Section 4.4. Successors and Assigns. All agreements of Merger Sub and Lehman Brothers in this Third Supplemental Indenture shall bind their respective successors. All agreements of the Trustee in this Third Supplemental Indenture shall bind its successor.

Section 4.5. Modification of Securities. In order to give effect to this Third Supplemental Indenture, the modification, annotation and/or exchange of the Securities shall be evidenced by a substitution of the relevant page thereto.

Section 4.6. Governing Law. THIS THIRD SUPPLEMENTAL INDENTURE AND THE SECURITIES WILL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

Section 4.7. Multiple Originals. The parties may sign any number of copies of this Third Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. One signed copy is enough to prove this Third Supplemental Indenture.

Section 4.8. Separability Clause. In case any provision in this Third Supplemental Indenture or the Securities shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

Section 4.9. Trustee. The Trustee makes no representations as to the validity or sufficiency of this Third Supplemental Indenture. The recitals and statements herein are deemed to be those of Lehman Brothers, Merger Sub and Old Neuberger and not of the Trustee.

[Signature page follows]

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IN WITNESS WHEREOF, the undersigned, being duly authorized, have executed this Third Supplemental Indenture on behalf of the respective parties hereto as of the date first above written.

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