[424B5] Lyra Therapeutics, Inc. Prospectus Supplement (Debt Securities)

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As Filed Pursuant to Rule 424(b)(5)
Registration No. 333-278163

PROSPECTUS SUPPLEMENT

(To Prospectus and Prospectus Supplement dated

April 1, 2024)

Common Stock

This prospectus supplement (the “Prospectus Supplement”) supplements the prospectus dated April 1, 2024 (the “Base Prospectus”) and the prospectus supplement dated April 1, 2024 (together with the Base Prospectus, the “ATM Prospectus”), relating to the offer and sale of shares of our common stock from time to time pursuant to the terms of the Amended and Restated Controlled Equity Offering^SM Sales Agreement, dated March 22, 2024 (the “Agreement”), with Cantor Fitzgerald & Co. (“Cantor”) as sales agent. This Prospectus Supplement should be read in conjunction with the ATM Prospectus. This Prospectus Supplement is qualified by reference to the ATM Prospectus, except to the extent that the information presented herein supersedes the information contained in the ATM Prospectus.

In accordance with the terms of the Agreement, we may offer and sell shares of our common stock from time to time through Cantor pursuant to at-the-market transactions, subject to the limitations described in the ATM Prospectus (the “ATM Program”). As of the date of this Prospectus Supplement, we have sold an aggregate of 7,059,228 shares of our common stock pursuant to the Agreement for aggregate gross proceeds of $24,835,145.28.

The purpose of this Prospectus Supplement is to suspend the ATM Program and to terminate the continuous offering by us under the ATM Prospectus effective on June 26, 2025. We will not make any sales of our common stock pursuant to the Agreement unless and until a new prospectus supplement is filed with the Securities and Exchange Commission. However, for the avoidance of doubt, the Agreement remains in full force and effect.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities or passed upon the adequacy or accuracy of this prospectus supplement or the accompanying prospectus. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is June 26, 2025.