Second Letter Agreement between Incannex Healthcare Inc. and Investor Regarding Waiver of Equity Sale and Registration Restrictions

Exhibit 10.1

May 27, 2025

Incannex Healthcare Inc.

8 Century Circuit, Suite 105 Norwest

Sydney, NSW 2153, Australia

Attention: Joel Latham

Re: Letter Agreement

Ladies and Gentlemen:

Reference is made to (i) that certain Registration Rights Agreement (the “Registration Rights Agreement”), dated as of March 7, 2025, by and between Incannex Healthcare, Inc. (the “Company”) and the undersigned (the “Investor”), (ii) that certain Securities Purchase Agreement, dated as of March 7, 2025 (the “Purchase Agreement”), by and between the Company and the Investor, entered into in connection with the Company’s private placement pursuant to the Purchase Agreement and other securities purchase agreements with certain institutional investors (collectively, with the Purchase Agreement, the “Purchase Agreements”) pursuant to which the Company sold Common Stock, Pre-Funded Warrants and Series A Warrants for gross proceeds of approximately $12.5 million (the “Private Placement”), (iii) the Series A Warrant issued pursuant to the Purchase Agreement by the Company to the Investor on March 10, 2025 (the “Series A Warrant”), and (iv) that certain at-the-market sales agreement, dated as of April 7, 2025, by and between the Company and A.G.P./Alliance Global Partners (“AGP”), with respect to the offer and sale of Common Stock from time to time, as it may be amended from time to time, including to add Curvature Securities, LLC (“Curvature”) as an additional sales agent thereunder (the “ATM Facility”). Capitalized terms used but not defined in this letter shall have the meanings ascribed to them in the Purchase Agreement.

Pursuant to Section 6(b) of the Registration Rights Agreement, the Company may not include any securities of the Company in any Registration Statements other than the Registrable Securities (as defined in the Registration Rights Agreement), and is prohibited from filing registration statements, subject to certain limited exceptions (the “Subsequent Registration Statement Restriction”), and must file any additional Registration Statements before the Filings Date (collectively, the “Filing Deadline”). The Company is subject to the restrictions set forth in Sections 4.12(a) and (b) of the Purchase Agreement (the “Subsequent Equity Sale Restrictions”), subject to certain exceptions set forth in Section 4.12(c) of the Purchase Agreement, including an exception for sales of Common Stock pursuant to the ATM Facility at a price no less than $1.08.

The Investor hereby waives the Subsequent Equity Sale Restrictions such that the Company may issue sell shares of Common Stock pursuant to the ATM Facility at any time from and after the date hereof and before the earlier of (i) the date that is 75 days after the date hereof and (ii) the fifth calendar day following the first public announcement of topline data from the Phase 2 portion of the RePOSA Phase 2/3 study of IHL-42X (such sales, the “Permitted ATM Sales” and such period of time, the “Permitted ATM Sales Period”), whether or not the sale price for such Permitted ATM Sales is greater than or less than $1.08. The Investor hereby further agrees that the definition of “Exempt ATM Facility” in the Purchase Agreement is hereby amended to mean an at-the-market sales agreement to implement an at-the-market sales facility with AGP and/or Curvature.

The Investor hereby waives the Subsequent Registration Statement Restriction and consents to the Company disclosing this letter agreement in its SEC Reports. The Investor also waives the Filing Deadline. Notwithstanding the foregoing, if, during the Permitted Sales Period, on the first Trading Day following any Trading Day on which (i) the official closing price of the Common Stock as reported by The Nasdaq Stock Market LLC for the immediately preceding Trading Day was $.40 per share or more and (ii) the aggregate trading volume of the Common Stock for the five-day period immediately proceeding the then-current Trading Day on the Trading Market on which the Common Stock is then listed or quoted as reported by Bloomberg L.P. (based on Trading Days commencing at 9:30 a.m. (New York City time) and ending at 4:02 p.m. (New York City time)) was $100 million or more (a “High Volume Day”), the Company fails to issue one or more Placement Notices (as defined in the ATM Facility) to AGP and/or Curvature requesting the placement of shares of Common Stock pursuant to the ATM Facility in an amount equal to at least 15% of the daily trading volume for such then-current Trading Day (based on a Trading Day commencing at 9:30 a.m. New York City time and ending at 4:02 p.m. New York City time and as reported by Bloomberg L.P.) pursuant to the ATM (or such lesser percentage as may be sufficient for the Net Proceeds (as defined below) from all Permitted ATM Sales to equal $11,268,731.28), the Filing Deadline shall be reimposed and extended to the date that is 10 calendar days immediately following such High Volume Day. If, on the last day of the Permitted ATM Sales Period, the number of Cancelled Warrant Shares is less than the number of Warrant Shares underlying the Series A Warrant, the Filing Deadline shall be reimposed and extended to the date that is 10 calendar days immediately following the last day of the Permitted ATM Sales Period.

At any time during the Permitted ATM Sales Period (but not after the Release Date (as defined in the Series A Warrants), if any), the Investor agrees that it shall not without the Company’s prior written consent (i) exercise the Series A Warrant, (ii) offer, sell, contract to sell, hypothecate, pledge or otherwise dispose of or offer to buy, buy, contract to by or otherwise acquire (or enter into any transaction which is designed to, or might reasonably be expected to, result in the acquisition or disposition (whether by actual acquisition or disposition or effective economic acquisition or disposition due to cash settlement or otherwise) by the Investor or any controlled Affiliate of the Investor or any person in privity with the Investor or any controlled Affiliate of the Investor), directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Exchange Act, with respect to, any shares of Common Stock of the Company or securities convertible, exchangeable or exercisable into, shares of Common Stock of the Company beneficially owned, held or hereafter acquired by the Investor (the “Securities”), (iii) enter into any discussions, negotiations, arrangements or understandings with any third party with respect to the foregoing or (iv) publicly disclose any intention, plan or arrangement to do any of the foregoing.

Any aggregate net proceeds to the Company from the Permitted ATM Sales, with such net proceeds being the gross proceeds less the placement agent fee of 3.0% of the gross proceeds to the Company from the Permitted ATM Sales and deal related legal expenses of up to $95,000 (the “Net Proceeds”), up to $11,268,731.28 in the aggregate during the Permitted ATM Sales Period, will be paid by the Company to the Investor and the other purchasers in the Private Placement, in accordance with the procedures set forth below, with the Investor receiving its pro rata portion of the Net Proceeds (based on the proportion the Investor’s Subscription Amount bears to the aggregate subscription amount of all purchasers in the Private Placement) received during the Permitted ATM Sales Period. In consideration of the Warrant Cancellation Payment, the number of Warrant Shares (as defined in the Series A Warrant) underlying the Series A Warrant, prior to any adjustments as set forth therein, shall be deemed to be reduced by a number of shares (the “Cancelled Warrant Shares”) equal to the quotient obtained by dividing the Warrant Cancellation Payment by $2.14, rounded down to the nearest whole share (the “Warrant Cancellation”). The Warrant Cancellation shall have the same effect as cancellation of the Series A Warrant and issuance of a new Series A Warrant evidencing the right to purchase any remaining number of Warrant Shares, or, if the number of Cancelled Warrant Shares equals the number of Warrant Shares underlying the Series A Warrant, the cancellation and termination of the Series A Warrant in its entirety. In addition, the Company will pay to the Investor and other purchasers in the Private Placement, in accordance with the procedures set forth below, with the Investor receiving its pro rata portion based on the proportion the Investor’s Subscription Amount bears to the aggregate subscription amount of all purchasers in the Private Placement, of $1,000,000 (which excludes the Net Proceeds of $12,499,828 payable pursuant to the Prior Letter Agreements (as defined below)) from sales and issuances pursuant to the ATM Facility which occurred prior to the date of this Letter Agreement. The payments due to the Investor pursuant to this paragraph shall collectively be referred to as the “Warrant Cancellation Payment.”

On the earlier of (i) the date the Company raises $11,268,731.28 in Net Proceeds from the Permitted ATM Sales or (ii) the last day of the Permitted ATM Sales Period, the Company shall provide a notice setting forth the amount of Net Proceeds, the amount of the Warrant Cancellation Payment and the number of Cancelled Warrant Shares (the “Permitted ATM Sale Notice”) to the Investor at the email address set forth in the Investor’s signature page to the Purchase Agreement. The Warrant Cancellation shall be immediately effective upon the delivery of the Permitted ATM Sale Notice. Within the earlier of (a) three Business Days after the end of the Permitted ATM Sales Period and (b) five Business Days after the delivery of the Permitted ATM Sale Notice, the Company shall pay the Warrant Cancellation Payment to the Investor pursuant to the wire instructions set forth on Exhibit A of that certain Letter Agreement, dated May 15, 2025 by and between the Company and the Investor (the “Prior Letter Agreement”).

If the number Cancelled Warrant Shares equals the number of Warrant Shares underlying the Series A Warrant, upon payment of the Warrant Cancellation Payment, each of the Registration Rights, Agreement, Purchase Agreement and Series A Warrant shall terminate in their entirety and be of no further force or effect.

In connection with the foregoing, the Investor represents and warrants to the Company that the Investor (a) is the sole owner of, and has good and lawful title to, the Series A Warrant free of any lien or encumbrance, except for restrictive legends relating to compliance with the Securities Act and (b) has all requisite authority to enter into this agreement and perform its obligations hereunder, including without limitation with respect to any Warrant Cancellation. The Investor further acknowledges and agrees that the Series A Warrant may not be sold, transferred, pledged or assigned unless, in addition to the other procedures set forth in the Series A Warrant, the recipient of the Series A Warrant agrees in writing to be subject all of the terms and conditions of this letter agreement as if it were an original party hereto.

The Company acknowledges and agrees that, except for the waivers, consents and agreements set forth above and in the Prior Letter Agreement, the surviving obligations under the Registration Rights Agreement, Series A Warrant and the Purchase Agreement remain unmodified and in full force and effect.

[Signature Pages Follows]

Very truly yours,

[●]

Signature Page To Letter Agreement

Acknowledged and accepted:

INCANNEX HEALTHCARE INC.

Signature Page To Letter Agreement