Lyra Therapeutics (LYRA) 8-KLyra Therapeutics Announces $50.0 Million Private Placement

Exhibit 4.1

Execution Version

LYRA THERAPEUTICS, INC.

AMENDMENT NO. 1 TO

NINTH AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT

This Amendment No. 1 to Ninth Amended and Restated Investor Rights Agreement, dated as of May 25, 2023 (this “Amendment”) is entered into by and among Lyra Therapeutics, Inc., a Delaware corporation (the “Company”), and the undersigned Investors party to the Ninth Amended and Restated Investor Rights Agreement, dated as of April 7, 2022 (the “Rights Agreement”), by and among the Company and the Investors party thereto. Capitalized terms used by not defined herein shall have the meanings ascribed to such terms in the Rights Agreement, as amended by this Amendment.

Recitals

WHEREAS, the Investors, concurrently herewith, are purchasing shares of the Company’s common stock, $0.001 par value per share (the “Common Stock”), and certain Common Stock purchase warrants to purchase shares of Common Stock, in each case, pursuant to that certain Securities Purchase Agreement of even date herewith (the “2023 Purchase Agreement”);

WHEREAS, the Investors’ obligations in the 2023 Purchase Agreement are conditioned upon the Company’s execution and delivery of this Amendment;

WHEREAS, subject to certain inapplicable exceptions, any term of the Rights Agreement may be amended or terminated and the observance of any term of the Rights Agreement may be waived (either generally or in a particular instance and either retroactively or prospectively), with the written consent of the Company and the holders of a majority of the Registrable Shares held by all of the Stockholders; and

WHEREAS, the parties to this Amendment hold the requisite number of shares to amend the Rights Agreement and desire to amend the Rights Agreement to provide for certain arrangements with respect to the registration of shares of capital stock of the Company under the Securities Act of 1933, as amended, as more specifically set forth herein.

NOW, THEREFORE, in consideration of the mutual promises and covenants contained herein and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

(a) The definition of “2023 Purchase Agreement” is hereby added to Section 1 of the Agreement directly before the definition of “Board of Directors” therein to read as follows:

““2023 Purchase Agreement” means that certain Securities Purchase Agreement, dated as of May 25, 2023, by and among the Company, certain of the Investors and the other purchasers party thereto.”

(b) The definition of “Registrable Shares” in Section 1 of the Agreement is hereby amended and restated in its entirety to read as follows:

““Registrable Shares” means (i) any shares of Common Stock held by an Investor or other Stockholder, and any shares of Common Stock issued or issuable upon the conversion or exercise of any other securities, in each case that were acquired by such Investor or other Stockholder prior to May 25, 2023, (ii) the shares of Common Stock purchased by an Investor pursuant to the Purchase Agreement, (iii) the shares of Common Stock purchased by an Investor pursuant to the 2023 Purchase Agreement, (iv) the shares of Common Stock issued or issuable upon exercise of the Purchase Warrants (as defined in the 2023 Purchase Agreement) purchased by an Investor pursuant to the 2023 Purchase Agreement and (v) any other shares of Common Stock issued in respect of the shares described in clauses (i) through (iv) above (because of stock dividends, splits or combinations of securities, reclassifications, recapitalizations, or similar events occurring after the date of this Agreement); provided, however, that shares of Common Stock which are Registrable Shares shall cease to be Registrable Shares upon (i) any sale pursuant to a Registration Statement or Rule 144 under the Securities Act, (ii) any sale in any manner to a person or entity which, by virtue of Section 4 of this Agreement, is not entitled to the rights provided by this Agreement or (iii) the termination with respect to such shares of registration rights pursuant to Section 2.11 of this Agreement.”

(a) Effectiveness of Amendment; Continuing Force and Effect. The Rights Agreement is hereby amended as described herein. Such amendment is effective upon execution of this Amendment by the Company and the Investors constituting the requisite votes necessary to amend the Rights Agreement. Except as expressly provided herein, all other terms and conditions of the Rights Agreement remain in full force and effect and are hereby ratified and confirmed.

(b) Governing Law. This Amendment shall be governed by and construed in accordance with the internal laws of the State of Delaware (without reference to the conflicts of law provisions thereof).

(c) Complete Agreement. The Rights Agreement, as amended by this Amendment, constitutes the entire agreement and understanding of the parties thereto with respect to the subject matter thereof and supersedes all prior agreements and understandings relating to such subject matter.

(d) Counterparts; Facsimile Signatures. This Amendment may be executed and delivered in any number of counterparts, each of which shall be deemed to be an original, and all of which together shall constitute one and the same document. Counterparts may be delivered via facsimile, electronic mail (including pdf or any electronic signature complying with the U.S. federal ESIGN Act of 2000, e.g., www.docusign.com) or other transmission method and any counterpart so delivered shall be deemed to have been duly and validly delivered and be valid and effective for all purposes.

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2

IN WITNESS WHEREOF, the parties have executed this Amendment as of the date first written above.

IN WITNESS WHEREOF, the parties have executed this Amendment as of the date first written above.

IN WITNESS WHEREOF, the parties have executed this Amendment as of the date first written above.