LOCK-UP LETTER AGREEMENT September 22, 2016

Exhibit 10.3

LOCK-UP LETTER AGREEMENT

September 22, 2016

Galectin Therapeutics Inc.

4960 Peachtree Industrial Boulevard

Suite 240

Norcross, GA 30071

Ladies and Gentlemen:

This Agreement contains restrictions related to the common stock (“Common Stock”) and preferred stock (“Preferred Stock”) of Galectin Therapeutics, Inc. (the “Company”). In consideration of the warrants described herein (the “Lock-Up Warrants”) to be issued by the Company to 10X Fund, L.P. (“10X Fund”) to purchase up to 1,000,000 shares of Common Stock and the Lock Up Warrant as described in the 2016 Securities Purchase Agreement (as hereinafter defined), and for other good and valuable consideration, 10X Fund hereby irrevocably agrees that, for a period commencing on the date hereof and ending on the eighteen (18) month anniversary of the date hereof (such 18 month period, the “Lock-Up Period”), without the prior written consent of the Company, 10X Fund will not, directly or indirectly, except as otherwise specified herein, (1) offer for sale, sell, contract to sell, pledge, or otherwise dispose of (or enter into any transaction or device that is designed to, or could be expected to, result in the disposition by any person at any time in the future of), directly or indirectly, any Lock-Up Securities (as hereinafter defined), (2) enter into any swap, hedge or other derivatives transaction that transfers to another, in whole or in part, any of the economic benefits or risks of ownership of shares of Lock-Up Securities, (3) enter into any “short sales” as defined in Rule 200 of Regulation SHO under the Exchange Act, whether any such transaction described in clause (1), (2) or (3) above is to be settled by delivery of Common Stock or other securities, in cash or otherwise, or (4) publicly disclose the intention to do any of the foregoing, except as set forth herein.

The term “Lock-Up Securities” shall mean any shares of Preferred Stock or Common Stock acquired by 10X Fund under that Securities Purchase Agreement between the Company and 10X Fund dated February 12, 2009 (the “2009 Purchase Agreement”) or under that Securities Purchase Agreement between the Company and 10X Fund dated September 22, 2016 (the “2016 Purchase Agreement” and with the 2009 Purchase Agreement, the “Purchase Agreements”), including without limitation any shares of Common Stock acquired as a result of dividends paid on Preferred Stock, upon conversion of Preferred Stock or upon exercise of warrants acquired under either Purchase Agreement; provided, however, that Lock-Up Securities shall not include any other securities of the Company of which 10X Fund may be deemed to be the beneficial owner with the Rules and Regulations of the Securities Exchange Act of 1934, as amended.

Notwithstanding the foregoing, (i) if during the last 17 days of the Lock-Up Period, the Company issues an earnings release or material news or a material event relating to the Company occurs or prior to the expiration of the Lock-Up Period the Company announces that it will release earnings results during the 16-day period beginning on the last day of the Lock-Up Period, then the restrictions imposed by this Lock-Up Letter Agreement shall continue to apply

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until the expiration of the 18-day period beginning on the issuance of the earnings release or the announcement of the material news or the occurrence of the material event, unless the Company waives such extension in writing.

No provision in this Lock-Up Letter Agreement shall be deemed to restrict or prohibit

10X Fund hereby further agrees that, (a) simultaneous with engaging in any transaction or taking any other action that is subject to the terms of this Lock-Up Letter Agreement during the period from the date of this Lock-Up Letter Agreement to and including the expiration of the Lock-Up Period (as such may have been extended pursuant to the third paragraph herein), it will give notice thereof to the Company and shall use reasonable best efforts not to complete the transaction if Company believes that the consummation of such transaction is not permitted by the prior paragraph; (b) it will provide in its governing documents that all limited partners in 10X Fund who contribute capital to fund the purchase of Lock-Up Securities under the 2016 Purchase Agreement are subject to lock-up terms at least as restrictive as those contained in this Lock-Up Letter Agreement, and (c) it will use its best efforts to obtain the consent of limited partners in 10X Fund who contributed capital to fund the purchase of Lock-Up Securities under the 2009 Purchase Agreement to agree not to withdraw their capital from the 10X Fund for the Lock-Up Period, except as permitted by the Quarterly Liquidity Program. The Company shall be a third party beneficiary of the agreements contemplated by clauses (b) and (c) above, which shall be referred to herein as the “LP Lock-Up.”

In furtherance of the foregoing, the Company and its transfer agent are hereby authorized to decline to make any transfer of securities if such transfer would constitute a violation or breach of this Lock-Up Letter Agreement.

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In consideration for the agreements of 10X Fund contained herein, the Company shall issue to 10X Fund the Lock-Up Warrants, which shall be in substantially the form attached hereto as Exhibit A. The Lock-Up Warrants shall be issued as follows:

The exercise price of the Lock-Up Warrants shall be equal to $3 per share, or such lesser price per share as is contained in the warrants issued under the 2016 Purchase Agreement. The form of the Lock-Up Warrants shall be the same as the form used for the warrants issued under the 2016 Purchase Agreement.

This agreement is irrevocable and shall be binding upon the undersigned and the assigns of the undersigned.

The undersigned hereby represents and warrants that the undersigned has full power and authority to enter into this Lock-Up Letter Agreement and that, 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 heirs, personal representatives, successors and assigns of the undersigned.

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