PURCHASE AGREEMENT

Exhibit 10.2

PURCHASE AGREEMENT

November 20, 2014

Invus, L.P.

Invus C.V.

Artal International S.C.A.

c/o The Invus Group, LLC

750 Lexington Avenue (30^th Floor)

New York, New York 10022

Lexicon Pharmaceuticals, Inc.

8800 Technology Forest Place

The Woodlands, Texas 77381

Attn:   President and Chief Executive Officer

Ladies and Gentlemen:

Reference is made to (a) the Stockholders’ Agreement, dated as of June 17, 2007 (as amended, supplemented or otherwise modified, the “Stockholders’ Agreement”), by and between Invus, L.P. ( “Invus, L.P.”) and Lexicon Pharmaceuticals, Inc. (the “Company”), (b) the Securities Purchase Agreement, dated as of June 17, 2007 (as amended, supplemented or otherwise modified, the “Securities Purchase Agreement”), by and between Invus, L.P. and the Company, and (c) that certain Underwriting Agreement being entered into by the Company with the representatives of the underwriters concurrently with this Agreement (the “Underwriting Agreement”) providing for the issuance by the Company to the underwriters (the “Public Stock Offering”) of 49,751,244 shares (the “Firm Shares”) of the Company’s common stock, par value $0.001 per share (the “Common Stock”), plus up to 7,462,687 additional shares of Common Stock pursuant to the underwriters’ option to purchase additional shares, for sale in a public offering at a price to the public of $1.005 per share (the “Purchase Price”). Capitalized terms used but not otherwise defined herein shall have the meanings ascribed to them in the Stockholders’ Agreement.

In consideration of the mutual covenants and agreements herein contained, and intending to be legally bound hereby, pursuant to Section 7.13 of the Stockholders’ Agreement, each of Invus, L.P. and Invus C.V. hereby waives its rights under Section 4.02 of the Stockholders’ Agreement to purchase shares of Common Stock in connection with the Public Stock Offering and in connection with the concurrent issuance by the Company to the initial purchasers of up to $95.0 million aggregate principal amount of the Company’s 5.25% Convertible Senior Notes due 2021 (which amount includes the initial purchasers’ option to purchase additional notes).

Subject to the satisfaction or waiver of the conditions described in Section IV, the Investor hereby agrees to purchase from the Company 149,253,731 shares of Common Stock (the “Shares”), at the Purchase Price per share. The total purchase price for the Shares shall be equal to $150,000,000.

The closing of the sale of the Shares shall take place concurrently with the closing of the sale of the Firm Shares under the Underwriting Agreement (the “Closing Date”), (i) with payment for the Shares to be made to the Company by wire transfer of immediately available funds on the Closing Date and (ii) with delivery of the Shares registered, as applicable, in the name of Artal International S.C.A. (the “Investor”) or its designees with the Securities Act legend set forth in Exhibit A attached thereto and otherwise free and clear of all liens, with any transfer or stamp taxes duly paid by the Company.

The Company hereby represents and warrants to and agrees with the Investor to all the same representations and warranties contained in Section 1 and the covenants contained in Section 6 (other than the last paragraph thereof) of the Underwriting Agreement mutatis mutandis to the same extent as if such representations and warranties and covenants were set forth herein for the benefit of the Investor instead of the underwriters party to the Underwriting Agreement (except that references to the Underwriting Agreement therein shall be references to this Agreement and references to the Shares thereunder shall be references to the Shares).

The Investor hereby represents and warrants to the Company that it (i) is acquiring the Shares for its own account solely for the purpose of investment and not with a view to, or for resale in connection with, any distribution of such Shares or any interest therein, (ii) is an “accredited investor” as defined in Rule 501 of Regulation D promulgated under the Securities Act, a sophisticated investor and, by virtue of its business or financial experience, is capable of evaluating the merits and risks of the investment in the Shares and (iii) has been provided an opportunity to ask questions of and receive answers from representatives of the Company concerning the terms and conditions of this Agreement and the purchase of the Shares contemplated hereby.

(a) As of the Closing Date, the Company shall have used its best efforts to cause the Shares to be listed on NASDAQ.

(b) Whether or not the transactions contemplated by this Agreement are consummated or this Agreement is terminated, the Company agrees to pay or cause to be paid the reasonable fees and expenses of Simpson Thacher & Bartlett LLP, counsel to Invus, L.P., Invus C.V. and the Investor, relating to the Public Stock Offering, the concurrent convertible notes offering by the Company (the “Notes Offering”) and the transactions contemplated by this Agreement within 15 days of the submission of any invoice with respect thereto.

The obligation of the Investor hereunder to purchase the Shares from the Company, and of the Company to sell the Shares to the Investor, will be subject to the satisfaction or waiver of the following conditions on or prior to the Closing Date:

(a) The satisfaction by the Company of the conditions set forth in Section 5 of the Underwriting Agreement (other than clauses (i) and (j) thereunder);

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(b) The substantially concurrent closing of the sale of the Firm Shares on the terms set forth in the Underwriting Agreement;

(c) The substantially concurrent closing of the Notes Offering on the terms set forth in the Purchase Agreement (as such term is defined in the Underwriting Agreement) relating thereto;

(d) The delivery to the Investor of opinions of counsel to the Company by the same counsel as set forth in Sections 5(c), (d) and (e) of the Underwriting Agreement in the form and substance acceptable to the Investor; and

(e) The delivery to the Investor of the officer’s certificate contemplated by Section 5(b) of the Underwriting Agreement.

These conditions are for the Investor’s sole benefit and may be waived by the Investor in its sole discretion.

This Agreement shall automatically terminate upon any termination of the Underwriting Agreement.

(a) The Company hereby agrees to indemnify and hold harmless each of the Investor, Invus, L.P. and Invus C.V. and each of their respective affiliates, directors, officers, agents and employees and each person, if any, who controls the Investor, Invus, L.P. and Invus C.V. within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act (collectively, the “Indemnitees”) from and against any and all losses, claims, damages and liabilities (including, without limitation, any legal or other expenses reasonably incurred in connection with defending or investigating any such action or claim) arising out of or relating to any of the transactions contemplated by this Agreement. For the avoidance of doubt and notwithstanding the foregoing, the Company shall not be deemed to indemnify and hold harmless the Indemnitees from and against any losses resulting from a decrease in the trading price of their Common Stock.

(b) The provisions of Sections 7.06, 7.07 and 7.14 of the Stockholders’ Agreement are incorporated herein by reference and shall apply to this Agreement mutatis mutandis.

(c) This Agreement may not be amended or modified except by an instrument in writing signed by, or on behalf of, the parties hereto.

(d) This Agreement shall be deemed to satisfy the Company’s obligations under the Stockholders’ Agreement with respect to the delivery of a Notice of Issuance with respect to the Firm Shares and any additional shares which may be issued and sold pursuant to the underwriters’ option to purchase additional shares under the Underwriting Agreement and shall constitute the Investors’ waiver of rights pursuant to Section 4.02 of the Stockholders’ Agreement.

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(e) This Agreement may be executed and delivered in one or more counterparts, and by the different parties hereto in separate counterparts, each of which when executed and delivered shall be deemed to be an original but all of which taken together shall constitute one and the same agreement.

(f) All notices and other communications hereunder shall be in writing and shall be given (and shall be deemed to have been duly given upon receipt) by delivery in person, by fax, by electronic transmission, by a recognized overnight courier service or by registered or certified mail (postage prepaid, return receipt requested) to the respective parties at the following addresses (or at such other address for a party as shall be specified in a notice given in accordance with this clause (f)):

if to the Investor, Invus, L.P. or Invus C.V.:

c/o The Invus Group, L.L.C.

750 Lexington Avenue (30^th Floor)

New York, New York 10022

Attention: Raymond Debbane

Christopher Sobecki

with a copy to:

Simpson Thacher & Bartlett LLP

425 Lexington Avenue

New York, New York 10017

Attention: Kenneth Wallach, Esq.

if to the Company:

Lexicon Pharmaceuticals, Inc.

8800 Technology Forest Place

The Woodlands, Texas 77381

Attention: President and Chief Executive Officer

with a copy to:

Vinson & Elkins L.L.P.

1001 Fannin Street, Suite 2500

Houston, Texas 77002-6760

Attention: David Palmer Oelman, Esq.

[Signature Page Follows]

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[Signature Page to Purchase Agreement]

EXHIBIT A

THE SECURITIES REPRESENTED BY THIS BOOK-ENTRY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. NO TRANSFER, SALE, ASSIGNMENT, PLEDGE, HYPOTHECATION OR OTHER DISPOSITION OF THE SECURITIES REPRESENTED BY THIS BOOK-ENTRY MAY BE MADE EXCEPT PURSUANT TO (A) A REGISTRATION STATEMENT EFFECTIVE UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR (B) AN EXEMPTION FROM REGISTRATION THEREUNDER IF THE COMPANY AND THE TRANSFER AGENT HAVE BEEN FURNISHED WITH DOCUMENTATION AS MAY REASONABLY BE REQUIRED BY THE COMPANY THAT SUCH TRANSFER, SALE, ASSIGNMENT, PLEDGE, HYPOTHECATION OR OTHER DISPOSITION IS NOT REQUIRED TO BE REGISTERED UNDER THE SECURITIES ACT.