INDUCEMENT AWARD AGREEMENT

Exhibit 10.7

INDUCEMENT AWARD AGREEMENT

THIS INDUCEMENT AWARD AGREEMENT (this “Award Agreement”) is made on May 1, 2009 by and between Constellation Energy Partners LLC, a Delaware limited liability company (“CEP”), and Lisa J. Mellencamp (“Executive”).

WHEREAS, the Board of Managers (the “Board”) of CEP has determined that it is in the best interests of CEP to grant inducement bonuses to, among other things, promote the interests of CEP by enhancing the ability of CEP and its subsidiaries to attract and retain the services of individuals who are essential for the growth and profitability of CEP and to encourage them to devote their best efforts to advancing the business of CEP and its subsidiaries;

WHEREAS, in order to induce Executive to enter into that certain Offer Letter, dated as of December 31, 2008, between Executive and CEP (the “Offer Letter”), CEP agreed to make an inducement grant to Executive of a number of restricted common units representing limited liability company interests in CEP (the “Grant”), which restricted common units, when coupled with an amount of cash, would equal $400,000 on the grant date; and

WHEREAS, the Board has determined that the Grant shall be comprised of 35,971 restricted common units (the “Restricted Units”) in satisfaction of CEP’s obligation under the Offer Letter to make an inducement grant, which number of Restricted Units is based on the closing price of the Common Units on the NYSE Arca Equities, Inc. on December 31, 2008; and

WHEREAS, CEP (for a limited purpose), Executive and CEP Services Company, Inc., a Delaware corporation and CEP’s wholly owned subsidiary (“CSCI”), are entering into that certain Employment Agreement, dated as of May 1, 2009 (the “Employment Agreement”) contemporaneously herewith, which agreement supersedes the Offer Letter;

WHEREAS, the Grant has been approved by the Compensation Committee of the Board and is being made pursuant to the exemption from securityholder approval provided in Rule 5.3(d)(5)(A) of the NYSE Arca Rules;

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

(a) Definitions. As used herein, the following terms shall have the meanings set forth below:

“Affiliate” means, with respect to any Person, any other Person that directly or indirectly through one or more intermediaries controls, is controlled by or is under common control with, the Person in question. As used herein, the term “control” means the possession, direct or indirect, of the power to direct or cause the direction of the management and policies of a Person, whether through ownership of voting securities, by contract or otherwise.

“Award Agreement” has the meaning set forth in the preamble hereto.

“Board” has the meaning set forth in the recitals to this Award Agreement.

“CEP” has the meaning set forth in the preamble to this Award Agreement.

“Closing Price” means the closing sales price of a Common Unit on the applicable date (or if there is no trading in the Common Units on such date, on the next preceding date on which there was trading) as reported in The Wall Street Journal (or other reporting service approved by the Committee). In the event Common Units are not publicly traded at the time such value is required to be made hereunder, the determination of Closing Price shall be made in good faith by the Committee.

“Code” means the Internal Revenue Code of 1986, as amended.

“Committee” means the Compensation Committee of the Board.

“Common Unit” means a common unit of CEP, representing limited liability company interests.

“Employment Agreement” has the meaning set forth in the recitals to this Award Agreement.

“Executive” has the meaning set forth in the preamble to this Award Agreement.

“Grant” has the meaning set forth in the recitals to this Award Agreement.

“Offer Letter” has the meaning set forth in the recitals to this Award Agreement.

“Person” means an individual or a corporation, limited liability company, partnership, joint venture, trust, unincorporated organization, association, government agency or political subdivision thereof or other entity.

“Restricted Period” means the period from May 1, 2009 to December 31, 2010.

“Restricted Units” has the meaning set forth in the recitals to this Award Agreement.

“Tranche” means either the First Tranche or Second Tranche, as such terms are defined in Section 2(b).

(b) Construction. In this Award Agreement, unless a clear contrary intention appears, (a) the words “herein,” “hereof” and “hereunder” and other words of similar import refer to this Award Agreement as a whole and not to any particular Section or other subdivision, (b) reference to any Section means such Section hereof and (c) the words “including” (and with correlative meaning “include”) means including, without limiting the generality of any description preceding such term.

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(a) Grant. CEP hereby grants to Executive all right, title and interest in and to the record and beneficial ownership of the Restricted Units, subject to the conditions described herein.

(b) Vesting. Subject to Section 3(c), all rights to the Restricted Units shall fully vest in Executive and the restrictions set forth in Section 3(c) and Section 3(d) shall lapse as follows:

(i) on January 1, 2010 with respect to 17,986 Restricted Units (the “First Tranche”); and

(ii) on January 1, 2011 with respect to 17,985 Restricted Units (the “Second Tranche”).

(c) Administration.

(i) Issuance. The Restricted Units awarded hereunder shall be evidenced in book-entry form in the name of Executive.

(ii) Sources of Common Units Deliverable Under Grant. Any Common Units delivered pursuant to this Award Agreement shall consist, in whole or in part, of Common Units acquired in the open market, from any Affiliate, CEP or any other Person, or any combination of the foregoing as determined by the Committee in its sole discretion.

(iii) Adjustments. In the event that the Committee determines that any distribution (whether in the form of cash, Common Units, other securities or other property), recapitalization, split, reverse split, reorganization, merger, consolidation, split-up, spin-off, combination, repurchase, or exchange of Common Units or other securities of CEP, issuance of warrants or other rights to purchase Common Units or other securities of CEP, or other similar transaction or event affects the Common Units such that an adjustment is determined by the Committee to be appropriate in order to prevent dilution or enlargement of the benefits or potential benefits intended to be made available under this Award Agreement, then the Committee shall, in such manner as it may deem equitable, adjust the number and type of Common Units (or other securities or property) subject to the Award Agreement hereunder or, if deemed appropriate by the Committee, make provision for a cash payment to Executive; provided, however, that the number of Common Units subject to the Grant shall always be a whole number; and, provided further, that the Committee shall not take any action otherwise authorized under this paragraph (b) to the extent that (i) such action would cause (A) the application of Section 409A of the Code to the Award Agreement or (B) create adverse tax consequences under Section 409A of the Code should that Code Section apply to the Award Agreement or (ii) except as permitted in Section 4, materially reduce the benefit to Executive without the consent of Executive.

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(a) Ownership Rights. Subject to the restrictions set forth herein, including Section 3(b), Executive is entitled to all voting and ownership rights applicable to the Restricted Units.

(b) Pre-vesting Distributions.

(i) Distribution Credits. Prior to vesting pursuant to Section 2(b), Executive shall, for each Tranche, receive book-entry distribution credits (“Distribution Credits”) for any distributions paid by CEP on Common Units.

(ii) Accumulation of Distribution Credits. Until a Tranche has vested pursuant to Section 2(b), CEP shall, upon payment of a distribution in respect of Common Units, record Distribution Credits in respect of that Tranche in an amount equal to (i) the number of Restricted Units in such Tranche multiplied by the per-unit distribution amount so paid, divided by (ii) the per-unit Closing Price on the payment date of such distribution.

(iii) Earning and Settlement of Distribution Credits. The Distribution Credits accumulated with respect to a Tranche shall be earned upon the vesting of such Tranche pursuant to Section 2(b). Upon vesting of a Tranche pursuant to Section 2(b), any Distribution Credits accumulated with respect to such Tranche shall, at the discretion of the Committee, be settled in cash or Common Units.

(A) For Distribution Credits to be settled in cash, the amount of such payment shall be equal to the aggregate number of earned Distribution Credits to be settled in cash multiplied by the per-unit Closing Price on the date such Tranche vests pursuant to Section 2(b).

(B) For Distribution Credits to be settled in Common Units, CEP shall issue a number of whole Common Units equal to the aggregate number of earned Distribution Credits to be settled in Common Units; provided, however, that any Distribution Credits that would have resulted in the issuance of a fractional Common Unit pursuant to this Section 3(b)(iii)(B), shall instead be settled in cash in accordance with Section 3(b)(iii)(A).

(c) Risk of Forfeiture.

(i) General. Subject to Section 3(c)(ii), upon termination of Executive’s employment with or services to CEP and its Affiliates (including CSCI) for any reason during the applicable Restricted Period, all Restricted Units not then vested pursuant to Section 2(b) and Distribution Credits not then earned pursuant to Section 3(b)(iii) shall be automatically forfeited by Executive. The Committee may, in its discretion, waive in whole or in part such forfeiture.

(ii) Employment Agreement. Notwithstanding Section 3(c)(i) and anything to the contrary herein, if Executive’s Employment Agreement (defined below) provides

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for a treatment of the Restricted Units and Distribution Credits that differs from Section 3(c)(i), the terms of Executive’s Employment Agreement shall control upon the termination of Executive’s employment by CEP or its Affiliates (including CSCI). “Employment Agreement” means that certain Employment Agreement, dated as of May 1, 2009, entered into by and among CEP, CSCI and Executive, as such agreement may be amended from time to time.

(d) Transfer Restrictions.

(i) Except as provided in Section 3(d)(iii), this Award Agreement shall be payable only to Executive during Executive’s lifetime, or to the person to whom Executive’s rights shall pass by will or the laws of descent and distribution.

(ii) Except as provided in Section 3(d)(iii), none of the Award Agreement, any Restricted Units or Distribution Credits may be assigned, alienated, pledged, attached, sold or otherwise transferred or encumbered by Executive and any such purported assignment, alienation, pledge, attachment, sale, transfer or encumbrance shall be void and unenforceable against CEP or any of its Affiliates.

(iii) The Restricted Units and Distribution Credits may be transferred by Executive without consideration to immediate family members or related family trusts, family limited partnerships or similar entities.

Except to the extent prohibited by applicable law, the Committee is hereby authorized to make adjustments in the terms and conditions of, and the criteria included in, this Award Agreement in recognition of unusual or nonrecurring events (including the events described in Section 2(c)(iii)) affecting CEP or the financial statements of CEP, or of changes in applicable laws, regulations, or accounting principles, whenever the Committee determines that such adjustments are appropriate in order to prevent dilution or enlargement of the benefits or potential benefits intended to be made available to Executive under this Award Agreement.

(a) Tax Withholding.

(i) CEP or any Affiliate is authorized to withhold from any payment due or transfer made pursuant to this Award Agreement or from any compensation or other amount owing to a Participant the amount (in cash, Common Units, other securities, Common Units that would otherwise be issued pursuant to this Award Agreement or other property) of any applicable taxes payable at the minimum statutory rate in respect of this Award Agreement, the lapse of restrictions thereon or any payment or transfer under the Award Agreement and to take such other action as may be necessary in the opinion of CEP to satisfy its withholding obligations for the payment of such taxes.

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(ii) All Common Units to be issued pursuant to this Award Agreement shall be net of tax withholding, such that the tax withholding obligation of Executive in respect of this Award Agreement and such Common Units is satisfied through the retention by CEP of a number of Common Units equal to Executive’s aggregate tax withholding obligation divided by the per-unit Closing Price for the date immediately prior to the date of such issuance of Common Units.

(iii) Executive agrees that, if he or she makes an election under Section 83(b) of the Code with regard to the Restricted Units, Executive will so notify CEP in writing within two (2) days after making such election.

(b) No Right to Employment or Services. Nothing in this Award Agreement shall be construed as granting Executive the right to be retained in the employ of CEP or any of its Affiliates. Subject to the terms of the Employment Agreement, CEP or an Affiliate may at any time dismiss Executive from employment, free from any liability or any claim under this Award Agreement other than as provided under Section 3(c)(ii).

(c) Governing Law. This Award Agreement is entered into under, and shall be governed for all purposes by, the laws of the State of Delaware, without reference to its choice of law provisions.

(d) Section 409A of the Code. Notwithstanding anything in this Award Agreement to the contrary, this Award Agreement (i) is designed to avoid application of Section 409A of the Code to the Award Agreement and (ii) is designed to avoid adverse tax consequences under Section 409A of the Code should that Section apply to this Award Agreement. If any provision hereof would result in the imposition of an applicable tax under Section 409A of the Code and related regulations and pronouncements, that provision will be reformed to the extent reformation would avoid imposition of the applicable tax and no action taken to comply with Section 409A of the Code shall be deemed to adversely affect Executive’s rights to the Restricted Units or to require Executive’s consent.

(e) Severability. If any provision in this Award Agreement is or becomes or is deemed to be invalid, illegal or unenforceable in any jurisdiction or as to any Person, or would disqualify the Award Agreement under any law deemed applicable by the Committee, such provision shall be construed or deemed amended to conform to the applicable laws, or if it cannot be construed or deemed amended without, in the determination of the Committee, materially altering the intent of the Award Agreement, such provision shall be stricken as to such jurisdiction or person and the remainder of the Award Agreement shall remain in full force and effect.

(f) Other Laws. The Committee may refuse to issue or transfer any Common Units or other consideration under this Award Agreement if, in its sole discretion, it determines that the issuance or transfer of such Common Units or such other consideration might violate any applicable law or regulation, the rules of the principal securities exchange on which the Common Units are then traded, or entitle CEP or an Affiliate to recover the same under Section 16(b) of the Securities Exchange Act of 1934, as amended, and any payment tendered to CEP by Executive, other holder or beneficiary shall be promptly refunded to the relevant Executive, holder or beneficiary.

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(g) No Trust or Fund Created. This Award Agreement shall not create or be construed to create a trust or separate fund of any kind or a fiduciary relationship between CEP or any participating Affiliate and Executive. To the extent that any Person acquires a right to receive payments or securities from CEP or any participating Affiliate pursuant to this Award Agreement, such right shall be no greater than the right of any general unsecured creditor of CEP or any participating Affiliate.

(h) No Fractional Units. No fractional Common Units shall be issued or delivered pursuant to this Award Agreement, and the Committee shall determine whether cash, other securities or other property shall be paid or transferred in lieu of any fractional Common Units or whether such fractional Common Units or any rights thereto shall be canceled, terminated or otherwise eliminated.

(i) Headings. Headings are given to the Sections and subsections of this Award Agreement solely as a convenience to facilitate reference. Such headings shall not be deemed in any way material or relevant to the construction or interpretation of this Award Agreement or any provision thereof.

(j) Facility Payment. Any amounts payable hereunder to any person under legal disability or who, in the judgment of the Committee, is unable to properly manage his financial affairs, may be paid to the legal representative of such person, or may be applied for the benefit of such person in any manner which the Committee may select, and CEP and its Affiliates shall be relieved of any further liability for payment of such amounts.

(k) Gender and Number. Words in the masculine gender shall include the feminine gender, the plural shall include the singular and the singular shall include the plural.

(l) No Guarantee of Tax Consequences. None of the Board, CEP, nor the Committee makes any commitment or guarantee to Executive that any federal, state or local tax treatment will apply or be available to any Person eligible for benefits under this Award Agreement.

(m) Certain Restrictions. By executing this Award Agreement, Executive acknowledges that he or she has access to all documents filed by CEP with the Securities and Exchange Commission and has been provided a reasonable opportunity to ask questions of and receive answers from representatives of CEP regarding such matters. Executive agrees that he or she will enter into such representations, warranties and agreements and shall execute such documents as CEP may reasonably request in order to comply with the securities law or any other applicable laws, rules or regulations or with the terms of this Award Agreement.

(n) No Waiver. No failure by either party hereto at any time to give notice of any breach by the other party of, or to require compliance with, any condition or provision of this Award Agreement shall be deemed a waiver of similar or dissimilar provisions or conditions at the same or at any prior or subsequent time.

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(o) Counterparts. This Award Agreement may be executed in one or more counterparts, each of which shall be deemed to be an original, but all of which together will constitute one and the same agreement.

(p) Notices. For purposes of this Award Agreement, notices and all other communications provided in this Award Agreement shall be in writing and shall be deemed to have been duly given when personally delivered or when mailed by United States registered or certified mail, return receipt requested, postage prepaid, or when sent by recognized overnight delivery service, addressed as follows:

If to CEP:

Constellation Energy Partners LLC

One Allen Center

500 Dallas Street, Suite 3200

Houston, TX 77002

Attention: Legal Department

If to Executive:

Lisa J. Mellencamp

One Allen Center

500 Dallas Street, Suite 3200

Houston, TX 77002

or to such other address as either party may furnish to the other in writing in accordance herewith, except that notices or changes of address shall be effective only upon receipt.

(q) Entire Agreement. This Award Agreement constitutes the entire agreement of the parties with regard to the subject matter hereof, and contains all the covenants, promises, representations, warranties and agreements between the parties with respect to such subject matter. Without limiting the scope of the preceding sentence, all understandings and agreements preceding the date of execution of this Award Agreement and relating to the subject matter hereof (including the Offer Letter) are hereby null and void and of no further force and effect, including all prior employment and severance agreements, if any, by and between the Company and Executive, but excluding those certain (i) Grant Agreement Relating to Notional Units - Executives, of even date herewith, by and between CEP and Executive and (ii) Employment Agreement, of even date herewith, by and among CEP, Executive and CEP Services Company, Inc. Any modification of this Award Agreement will be effective only if it is in writing and signed by both parties.

[Signature page follows]

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IN WITNESS WHEREOF, the parties hereto have executed this Award Agreement to be effective as of May 1, 2009.

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