EX-7.4

Exhibit 7.4

Lock-Up Agreement

Reata Pharmaceuticals, Inc.

Public Offering of Common Stock

July 13, 2018

Jefferies LLC

Leerink Partners LLC

Stifel, Nicolaus & Company, Incorporated

As Representatives of the several Underwriters,

c/o Jefferies LLC

520 Madison Avenue

New York, New York 10022

c/o Leerink Partners LLC

299 Park Avenue, 21st Floor

New York, New York 10171

c/o Stifel, Nicolaus & Company, Incorporated

787 7th Avenue, 11th Floor

New York, New York 10019

Ladies and Gentlemen:

This letter is being delivered to you in connection with the proposed Underwriting Agreement (the “Underwriting Agreement”) between Reata Pharmaceuticals, Inc., a Delaware corporation (the “Company”), and Jefferies LLC, Leerink Partners LLC and Stifel, Nicolaus & Company, Incorporated (together, the “Representatives”) as representatives of a group of Underwriters named therein, relating to an underwritten public offering of Class A common stock, $0.001 par value per share (the “Common Stock”), of the Company (the “Offering”).

In order to induce you and the other Underwriters to enter into the Underwriting Agreement, the undersigned will not, without the prior written consent of the Representatives, offer, sell, contract to sell, pledge or otherwise dispose of (or enter into any transaction which is designed to, or might reasonably be expected to, result in the disposition (whether by actual disposition or effective economic disposition due to cash settlement or otherwise) by the undersigned or any affiliate of the undersigned or any person in privity with the undersigned or any affiliate of the undersigned), directly or indirectly, including the filing (or participation in the filing) of a registration statement with the Securities and Exchange Commission in respect of, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the Securities and Exchange Commission promulgated thereunder with respect to, any shares of capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock, or publicly announce an intention to effect any such transaction, for a period from the date hereof to and including the date 90 days after the signing date of the Underwriting Agreement (the “Lock-Up Period”).

The provisions of the immediately preceding paragraph shall not apply to or prohibit any of the following: (i) transfers, dispositions, or distributions of shares of capital stock of the Company by the undersigned (or any security convertible into or exercisable or exchangeable for shares of capital stock) (a) as a bona fide gift, (b) to limited partners, members, stockholders or trust beneficiaries of the undersigned or to any investment fund or other entity controlled or managed by the undersigned, (c) by will or other testamentary document or by intestacy, and (d) to any trust for the direct or indirect benefit of the undersigned or the immediate family of the undersigned (for the purposes of this letter, “immediate family” shall mean any relationship by blood, current or former marriage or adoption, not more remote than first cousin) in a transaction not involving a disposition for value, provided that, in the case of any transfer, disposition or distribution pursuant to the above four subclauses, each donee, transferee or distributee shall sign and deliver a lock-up letter in the form of this letter, and with respect to (a), (b) and (d) above, no filing under Section 16(a) of the Exchange Act, or other public announcement, reporting a reduction in beneficial ownership of shares of capital stock of the Company, shall be required or shall be voluntarily made by the undersigned or any other person in connection therewith during the Lock-Up Period; (ii) the exercise of options to purchase shares of capital stock of the Company granted under any stock incentive plan or stock purchase plan described (including through incorporation by reference) in the prospectus filed in connection with the Offering, provided that the underlying shares issuable upon exercise thereof shall continue to be subject to the restrictions on transfer set forth in this letter; (iii) transfers of shares of capital stock of the Company to the Company in connection with the termination of the undersigned’s employment with the Company; (iv) establishment of a trading plan pursuant to Rule 10b5-1 under the Exchange Act for the transfer of shares of capital stock of the Company, provided that such plan does not provide for the transfer of such capital stock during the Lock-Up Period and no filing under the Exchange Act or other public announcement shall be required or shall be voluntarily made by the undersigned or any other person in connection therewith during the Lock-Up Period; (v) transfers or dispositions of shares of Common Stock purchased on the open market following the Offering; (vi) transfers of shares of capital stock of the Company pursuant to a bona fide third-party tender offer for all outstanding shares of capital stock of the Company, merger, consolidation or other similar transaction made to all holders of the Company’s capital stock involving a change of control of the Company that has been approved by the board of directors of the Company, provided that (a) the shares of capital stock of the Company held by the undersigned that are not transferred pursuant to such tender offer, merger, consolidation or other similar transaction shall remain subject to all of the restrictions set forth in this letter, (b) if such transaction is not completed, all shares of capital stock of the Company held by the undersigned shall remain subject to the provisions of this letter, and (c) for purposes of this paragraph, “change of control” shall mean the consummation of any bona fide third party tender offer for any and all of the Company’s share capital or any merger, consolidation or other similar transaction the result of which is that any “person” (as defined in Section 13(d)(3) of the Exchange Act), or group of persons, other than the Company, becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 of the Exchange Act) of 50% of the total voting power of the voting securities of the Company; or (v) any conversion of shares of one class of the Company’s capital stock into shares of any class of the Company’s capital stock pursuant to the conversion rights applicable to the class of shares being so converted.

If any percentage of the shares of capital stock of the Company (or any security convertible into or exercisable or exchangeable for shares of such capital stock) held by any person or entity (other than the undersigned) that (1) is the holder of 2% or more of the outstanding shares of the Company’s capital stock (calculated on a fully-diluted, post-Offering basis) or (2) is a director or officer of the Company, that is subject to a lock-up agreement related to the Offering similar in form to this Lock-Up Agreement is released from any restrictions set forth in such lock-up agreement during the Lock-Up Period, the same percentage of shares of capital stock and such other securities held by the undersigned shall be immediately and fully released on the same terms from the lock-up restrictions set forth herein (the “Pro-rata Release”); provided, however, that such Pro-rata Release shall not occur (a) unless and until the Representatives have first waived such restrictions with respect to an aggregate number of shares of capital stock and such other securities representing more than 2 % of the Company’s total outstanding shares of Common Stock calculated as of immediately following the closing of the Offering and assuming conversion, exercise and exchange of all securities convertible into or exercisable or exchangeable for Common Stock, or (b) in the event of a release in connection with any underwritten public offering, whether or not such offering or sale is wholly or partially a secondary offering of the Company’s Common Stock during the Lock-Up Period (the “Underwritten Sale”); provided, however, that the undersigned, to the extent the undersigned has a contractual right to demand or require the registration of the undersigned’s Common Stock or such other securities or otherwise “piggyback” on a registration statement filed by the Company for the offer and sale of securities, is offered the opportunity to participate on a basis consistent with such contractual rights in such Underwritten Sale. In the event that the undersigned is released from any of its obligations under this letter or, by virtue of this letter, becomes entitled to offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, or otherwise transfer or dispose of, directly or indirectly, any shares of capital stock (or any securities convertible into or exercisable or exchangeable for shares of such capital stock) prior to the date that is 90 days after the signing date of the Underwriting Agreement, the Representatives shall use their commercially reasonable efforts to notify the undersigned within three (3) business days; provided that the failure to give such notice shall not give rise to any claim or liability against the Representatives or the Underwriters.

If for any reason the Underwriting Agreement shall be signed and then terminated prior to the Closing Date (as defined in the Underwriting Agreement), the agreement set forth above shall likewise be terminated, and the agreement set forth above shall automatically terminate if the Underwriting Agreement has not been entered into between the Representatives and the Company prior to September 15, 2018.

[Signature page follows]

Yours very truly,

/s/ William E. Rose

Name: William E. Rose

Capacity: Director

Address: 3963 Maple Avenue, Suite 200

Dallas, Texas 75219

LOCK-UP AGREEMENT