Amendment No. 1 to Incannex Healthcare Inc. 2023 Equity Incentive Plan

Exhibit 10.2

AMENDMENT NO. 1

TO

INCANNEX HEALTHCARE INC.

2023 EQUITY INCENTIVE PLAN

In accordance with those certain resolutions adopted by the Board of Directors and stockholders of Incannex Healthcare Inc., a Delaware corporation (the “Company”), the Incannex Healthcare Inc. 2023 Equity Incentive Plan (the “Plan”) is hereby amended as follows:

1. Section 5(b) of the Plan is hereby amended and restated in its entirety to increase the number of shares of the Company’s common stock, par value $0.0001 per share, reserved for issuance under the Plan as follows:

“(b) Subject to Section 13 of the Plan, Awards granted under the Plan shall be subject to the following limitations: (i) the Committee is authorized to deliver under the Plan an aggregate of 7,943,329 Common Shares; (ii) the Common Shares shall increase automatically on August 1, 2025 in an amount equal to 20% of the then outstanding Common Shares on August 1, 2025, and will further increase on the first day of each fiscal year of the Company (each, a “Fiscal Year”) beginning with the 2026 Fiscal Year commencing on July 1, 2026 and ending on (and including) the first day of the 2032 Fiscal Year commencing on July 1, 2032, in an amount equal to 5% of the then-outstanding shares of common stock on such dates (each, an “Evergreen Increase”); provided, however, that the Board may act to provide that there will be no Evergreen Increase for a Fiscal Year, or that the Evergreen Increase for such Fiscal Year will be a lesser number of shares of common stock; (iii) in no event shall the maximum aggregate number of Common Shares that may be issued under the Plan pursuant to Incentive Stock Options exceed the aggregate number of Common Shares set forth in Section 5(b)(i) of the Plan plus, to the extent allowable under Code Section 422 and the regulations promulgated thereunder, any Common Shares that again become available for issuance pursuant to Section 5(c) of the Plan; and (iv) the maximum number of Common Shares that may be granted under the Plan during any single fiscal year to any Participant who is a non-employee director, when taken together with any cash fees paid to such non-employee director during such year in respect of his or her Service as a non-employee director (including Service as a member or chair of any committee of the Board), shall not exceed $750,000 in total value (calculating the value of any such Awards based on the grant date fair value of such Awards for financial reporting purposes); provided that the non-employee directors who are considered independent (under the rules of The NASDAQ Stock Market or other securities exchange on which the Common Shares are traded) may make exceptions to this limit for a non-executive chair of the Board, if any, in which case the non-employee Director receiving such additional compensation may not participate in the decision to award such compensation.”

2. Unless otherwise expressly provided for in this Amendment to the Plan (this “Amendment”), all capitalized words, phrases, or defined terms used in this Amendment will have the same meaning ascribed to them in the Plan.

3. Except as expressly set forth in this Amendment, there have been no other changes or modifications to the Plan, and the Plan remains otherwise unchanged and in full force and effect.

4. This Amendment shall be effective as of May 27, 2025.

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IN WITNESS WHEREOF, the undersigned has caused this Amendment to be executed effective as of the date set forth above.

[Signature Page to Amendment to the Plan]