Form of Lock-Up Agreement

Exhibit 10.31

Form of Lock-Up Agreement

October [_], 2024

Univest Securities, LLC

75 Rockefeller Plaza, Suite 1838

New York, New York 10019

Ladies and Gentlemen:

The undersigned, an officer, director and/or a holder of shares of common stock, $0.001 par value per share (the “Common Stock”), or rights to acquire Common Stock, of Qualigen Therapeutics, Inc. (the “Company”), understands that you are the placement agent (the “Placement Agent”) named in the final form of the placement agency agreement (the “Placement Agency Agreement”) to be entered into among the Placement Agent and the Company, providing for the public offering (the “Public Offering”) of shares of Common Stock and if applicable, other securities (collectively, the “Securities”) pursuant to a registration statement filed or to be filed with the U.S. Securities and Exchange Commission (the “SEC”). Capitalized terms used herein and not otherwise defined shall have the meanings set forth for them in the Placement Agency Agreement.

In consideration of the Placement Agent’s agreement to enter into the Placement Agency Agreement and to proceed with the Public Offering, and for other good and valuable consideration, receipt of which is hereby acknowledged, the Undersigned hereby agrees, for the benefit of the Company and the Placement Agent that, without the prior written consent of the Placement Agent, the Undersigned will not, during the period commencing on the date of this Lock-up Agreement and continuing and including the date that is six (6) months after the date of the Placement Agency Agreement (the “Lock-Up Period”), unless otherwise provided herein, directly or indirectly (a) offer, sell, agree to offer or sell, solicit offers to purchase, grant any call option or purchase any put option with respect to, pledge, encumber, assign, borrow or otherwise dispose of (each a “Transfer”) any Relevant Security (as defined below) or otherwise publicly disclose the intention to do so, or (b) establish or increase any “put equivalent position” or liquidate or decrease any “call equivalent position” with respect to any Relevant Security (in each case within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations thereunder) with respect to any Relevant Security or otherwise enter into any swap, derivative or other transaction or arrangement that Transfers to another, in whole or in part, any economic consequence of ownership of a Relevant Security, whether or not such transaction is to be settled by the delivery of Relevant Securities, other securities, cash or other consideration, or otherwise publicly disclose the intention to do so. As used herein, the term “Relevant Security” means any Share, any warrant to purchase Shares or any other security of the Company or any other entity that is convertible into, or exercisable or exchangeable for, Shares or any other equity security of the Company, in each case owned beneficially or otherwise by the Undersigned on the date of closing of the Public Offering or acquired by the Undersigned during the Lock-Up Period.

[Signature page to Lock-Up Agreement]

The restrictions in the foregoing paragraph shall not apply to (a) any exercise (including a cashless exercise or broker-assisted exercise and payment of tax obligations), vesting or settlement, as applicable, by the Undersigned of options or warrants to purchase Shares or other equity awards pursuant to any share incentive or award plan or share purchase plan of the Company; provided that any Shares received by the Undersigned upon such exercise, conversion or exchange will be subject to the Lock-Up Period, (b) any establishment of a trading plan pursuant to Rule 10b5-1 under the Exchange Act for the Transfer of Shares (a “Trading Plan”); provided that (i) the Trading Plan shall not provide for or permit any Transfers, sales or other dispositions of Shares during the Lock-Up Period and (ii) the Trading Plan would not require any filing under Section 16(a) of the Exchange Act and no such filing is voluntarily made, (c) any Transfer of Shares acquired in open market transactions following the closing of the Public Offering, provided the Transfer would not require any filing under Section 16(a) of the Exchange Act and no such filing is voluntarily made, (d) the Transfer of the Undersigned’s Shares or any security convertible into or exercisable or exchangeable for shares of Common Stock to the Company in connection with the termination of the Undersigned’s employment with the Company or pursuant to contractual arrangements under which the Company has the option to repurchase such shares, provided that no filing by any party under the Exchange Act shall be required or shall be made voluntarily within 45 days after the date the Undersigned ceases to provide services to the Company, and after such 45^th day, if the Undersigned is required to file a report under the Exchange Act reporting a reduction in beneficial ownership of shares of Common Stock during the Lock-Up Period, the Undersigned shall clearly indicate in the footnotes thereto that the filing relates to the termination of the Undersigned’s employment, and no other public announcement shall be made voluntarily in connection with such transfer (other than the filing on a Form 5 made after the expiration of the Lock-Up Period), (e) the conversion of the outstanding securities into Shares, provided that any such Shares received upon such conversion shall be subject to the restrictions on Transfer set forth in this Lock-Up Agreement, or (f) the Transfer of Shares or any security convertible into or exercisable or exchangeable for Shares pursuant to a bona fide third-party tender offer for securities of the Company, merger, consolidation or other similar transaction that is approved by the board of directors of the Company, made to all holders of shares of Common Stock involving a change of control (as defined below), provided that all of the Undersigned’s Relevant Securities subject to this Lock-Up Agreement shall remain subject to the restrictions herein. For purposes of this Lock-Up Agreement, “change of control” means any bona fide third-party tender offer, merger, consolidation, or other similar transaction, in one transaction or a series of related transactions, the result of which is that any “person” (as defined in Section 13(d)(3) of the Exchange Act), or group of affiliated persons, other than the Company, becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 of the Exchange Act) of 50% or more of the total voting power of the voting shares of the Company (or the surviving entity).

In addition, the Undersigned further agrees that, except for the Registration Statement or any registration statement on Form S-8, during the Lock-Up Period, the Undersigned will not, without the prior written consent of the Placement Agent: (a) file or participate in the filing with the SEC any registration statement or circulate or participate in the circulation of any preliminary or final prospectus or other disclosure documents, in each case with respect to any proposed offering or sale of a Relevant Security beneficially owned by the Undersigned, or (b) exercise any rights the Undersigned may have to require registration with the SEC of any proposed offering or sale of a Relevant Security beneficially owned by the Undersigned.

In furtherance of the Undersigned’s obligations hereunder, the Undersigned hereby authorizes the Company during the Lock-Up Period to cause the transfer agent for the Relevant Securities to decline to Transfer, and to note stop transfer restrictions on the register of members and other records relating to, Relevant Securities for which the Undersigned is the record owner and the Transfer of which would be a violation of this Lock-Up Agreement and, in the case of the Relevant Securities for which the Undersigned is the beneficial owner but not the record owner, the Undersigned agrees that, during the Lock-Up Period, it will use its reasonable best efforts to cause the record owner to authorize the Company to cause the relevant transfer agent to decline to transfer and to note stop transfer restrictions on the register of members and other records relating to such Relevant Securities to the extent such transfer would be a violation of this Lock-Up Agreement.

Notwithstanding the foregoing or anything contained herein to the contrary, the Undersigned may Transfer the Undersigned’s Relevant Securities:

provided, in the case of clauses (i)-(vi), that (A) such transfer shall not involve a disposition for value, (B) the transferee agrees in writing with the Placement Agent and the Company to be bound by the terms of this Lock-Up Agreement and (C) such transfer would not require any filing under Section 16(a) of the Exchange Act and no such filing is voluntarily made.

For purposes of this Lock-Up Agreement, “immediate family” shall mean any relationship by blood, marriage, or adoption, not more remote than the first cousin.

If the Undersigned is an officer or director of the Company, (i) the Placement Agent agrees that at least three business days before the effective date of any release or waiver of the foregoing restrictions in connection with a Transfer of Shares, the Placement Agent will notify the Company of the impending release or waiver substantially in the form of Exhibit A hereto and (ii) the Company has agreed in the Placement Agency Agreement to announce the impending release or waiver by press release substantially in the form of Exhibit B hereto through a major news service at least two (2) business days before the effective date of the release or waiver. Any release or waiver granted by the Placement Agent hereunder to any such officer or director shall only be effective two (2) business days after the publication date of such press release. The provisions of this paragraph will not apply if (a) the release or waiver is effected solely to permit a transfer not for consideration and (b) the transferee has agreed in writing to be bound by the same terms described in this Lock-Up Agreement to the extent and for the duration that such terms remain in effect at the time of the transfer.

The Undersigned, whether or not participating in the Public Offering, understands that the Placement Agent is entering into the Placement Agency Agreement and proceeding with the Public Offering in reliance upon this Lock-Up Agreement.

The Undersigned hereby represents and warrants that the Undersigned has full power and authority to enter into this Lock-Up Agreement and that this Lock-Up Agreement has been duly authorized (if the Undersigned is not a natural person) and constitutes the legal, valid, and binding obligation of the Undersigned, enforceable in accordance with its terms. Upon request, the Undersigned will execute any additional documents necessary in connection with the enforcement hereof. Any obligations of the Undersigned shall be binding upon the successors and assigns of the Undersigned from the date of this Lock-Up Agreement.

This Agreement shall be delivered to the Placement Agents prior to the execution of the Placement Agency Agreement and shall automatically terminate upon the earliest to occur, if any, of (1) either the Placement Agent, on the one hand, or the Company, on the other hand, advising the other in writing, they have determined not to proceed with the Offering, (2) termination of the Placement Agency Agreement before the sale of the Securities, (3) the withdrawal of the Registration Statement or (4) the termination of the Offering prior to the sale of the Securities.

This Lock-Up Agreement shall be governed by and construed in accordance with the laws of the State of New York, without regard to the conflict of laws principles thereof. Delivery of a signed copy of this Lock-Up Agreement by facsimile or e-mail/.pdf transmission shall be effective as the delivery of the original hereof.

[Signature page follows]

[Signature page to Lock-Up Agreement]

EXHIBIT A

FORM OF WAIVER OF LOCK-UP

, 2024

[Name and Address of

Officer or Director

Requesting Waiver]

Dear Mr./Ms. [Name]:

This letter is being delivered to you in connection with the offering by QUALIGEN THERAPEUTICS, INC. (the “Company”) of shares of its common stock, par value $0.001 (the “Common Stock”), and the lock-up agreement dated , 2024 (the “Lock-up Agreement”), executed by you in connection with such offering, and your request for a [waiver] [release] dated , 2024, with respect to [●] shares of Common Stock (the “Shares”).

The undersigned hereby agree to [waive] [release] the transfer restrictions set forth in the Lock-up Agreement, but only with respect to the Shares, effective , 2024; provided, however, that such [waiver] [release] is conditioned on the Company announcing the impending [waiver] [release] by press release through a major news service at least two (2) business days before effectiveness of such [waiver] [release]. This letter will serve as notice to the Company of the impending [waiver] [release].

Except as expressly [waived] [released] hereby, the Lock-up Agreement shall remain in full force and effect.

EXHIBIT B

FORM OF PRESS RELEASE

QUALIGEN THERAPEUTICS, INC.

[Date]

Qualigen Therapeutics, Inc. (the “Company”) today announced that Univest Securities, LLC, the placement agent in the Company’s public offering of [●] shares of common stock is [waiving][releasing] a lock-up restriction with respect to [●] shares (the “Shares”) of the Company held by [certain officers or directors] [an officer or director] of the Company. The [waiver][release] will take effect on , 2024, and the Shares may be sold on or after such date.

This press release is not an offer for sale of the securities in the United States or in any other jurisdiction where such offer is prohibited, and such securities may not be offered or sold in the United States absent registration or an exemption from registration under the United States Securities Act of 1933, as amended.