Filed by Extra Space Storage Inc.

Pursuant to Rule 425 Under the Securities Act of 1933

And Deemed Filed Pursuant to Rule 14a-12

Under the Securities Exchange Act of 1934

Subject Company: Life Storage, Inc.

(Subject Company Commission File No.: 001-13820)

This filing relates to the proposed merger involving Extra Space Storage Inc., a Maryland corporation (“Extra Space”), Extra Space Storage LP, a Delaware limited partnership (“Parent OP”), Eros Merger Sub, LLC, a Delaware limited liability company and a wholly owned subsidiary of Parent (“Extra Space Merger Sub”), Eros OP Merger Sub, LLC, a Delaware limited liability company and a wholly owned subsidiary of Parent OP (together with Parent, Parent OP and Extra Space Merger Sub, the “Parent Parties”), Life Storage, Inc., a Maryland corporation (the “Life Storage”), and Life Storage LP, a Delaware limited partnership (the “Partnership” and, together with Life Storage, the “Acquired Parties”), pursuant to the terms of that certain Agreement and Plan of Merger, dated as of April 2, 2023, as amended on May 18, 2023, by and among the Parent Parties and the Acquired Parties.

Extra Space Storage Inc. Announces Dividend on Common Stock

SALT LAKE CITY, July 3, 2023 — Extra Space Storage Inc. (“EXR” or the “Company”) (NYSE: EXR) announced today that the Company’s board of directors has declared a dividend of $1.01 per share on the common stock of the Company, as permitted by the terms of the merger agreement the Company entered into with Life Storage, Inc. (“Life Storage” or “LSI”) (NYSE: LSI). The dividend is payable on July 19, 2023 to stockholders of record at the close of business on July 13, 2023.

Furthermore, it is anticipated that, following the closing of the merger with LSI, EXR will pay an additional dividend for the third quarter, keeping with EXR’s customary quarterly dividend timing. The pre-closing dividend will be attributed to the total amount paid for the third quarter, so that between this pre-closing dividend and the additional quarterly dividend to be paid, an EXR stockholder will receive a total dividend consistent with the amount that the EXR board of directors would have otherwise declared for the whole third quarter absent the closing.

About Extra Space Storage Inc.

Extra Space Storage Inc., headquartered in Salt Lake City, is a fully integrated, self-administered and self-managed real estate investment trust, and a member of the S&P 500. As of March 31, 2023, the Company owned and/or operated 2,388 self-storage properties, which comprise approximately 1.7 million units and approximately 180.0 million square feet of rentable storage space offering customers conveniently located and secure storage units across the country, including boat storage, RV storage and business storage. The Company is the second largest owner and/or operator of self-storage properties in the United States and is the largest self-storage management company in the United States.

1

Forward-Looking Statements

The statements in this communication that are not historical facts are forward-looking statements within the meaning of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended. These forward-looking statements are based on current expectations, estimates and projections about the industry and markets in which EXR and LSI operate as well as beliefs and assumptions of EXR and LSI. Such statements involve uncertainties that could significantly impact EXR’s or LSI’s financial results. Words such as “expects,” “anticipates,” “intends,” “plans,” “believes,” “seeks,” and “estimates,” including variations of such words and similar expressions, are intended to identify such forward-looking statements, which generally are not historical in nature. All statements that address operating performance, events or developments that EXR or LSI expects or anticipates will occur in the future — including statements relating to any possible transaction between EXR and LSI, acquisition and development activity, disposition activity, general conditions in the geographic areas where EXR or LSI operate, timing and amount of dividend payments and EXR’s and LSI’s respective debt, capital structure and financial position — are forward-looking statements. These statements are not guarantees of future performance and involve certain risks, uncertainties and assumptions that are difficult to predict. Although EXR and LSI believe the expectations reflected in any forward-looking statements are based on reasonable assumptions, neither EXR nor LSI can give assurance that its expectations will be attained and, therefore, actual outcomes and results may differ materially from what is expressed or forecasted in such forward-looking statements. Some of the factors that may affect outcomes and results include, but are not limited to: (i) EXR’s and LSI’s ability to complete the proposed transaction on the proposed terms or on the anticipated timeline, or at all, including risks and uncertainties related to securing the necessary stockholder approvals and satisfaction of other closing conditions to consummate the proposed transaction; (ii) the occurrence of any event, change or other circumstance that could give rise to the termination of the merger agreement relating to the proposed transaction; (iii) risks related to diverting the attention of EXR and LSI management from ongoing business operations; (iv) failure to realize the expected benefits of the proposed transaction; (v) significant transaction costs and/or unknown or inestimable liabilities; (vi) the risk of shareholder litigation in connection with the proposed transaction, including resulting expense or delay; (vii) the risk that LSI’s business will not be integrated successfully or that such integration may be more difficult, time-consuming or costly than expected; (viii) risks related to future opportunities and plans for the combined company, including the uncertainty of expected future financial performance and results of the combined company following completion of the proposed transaction; (ix) the effect of the announcement of the proposed transaction on the ability of EXR and LSI to operate their respective businesses and retain and hire key

2

personnel and to maintain favorable business relationships; (x) risks related to the market value of the EXR common stock to be issued in the proposed transaction; (xi) other risks related to the completion of the proposed transaction and actions related thereto; (xii) national, international, regional and local economic and political climates and conditions; (xiii) changes in global financial markets and interest rates; (xiv) increased or unanticipated competition for EXR’s or LSI’s properties; (xv) risks associated with acquisitions, dispositions and development of properties, including increased development costs due to additional regulatory requirements related to climate change; (xvi) maintenance of Real Estate Investment Trust status, tax structuring and changes in income tax laws and rates; (xvii) availability of financing and capital, the levels of debt that EXR and LSI maintain and their credit ratings; (xviii) environmental uncertainties, including risks of natural disasters; (xix) risks related to the coronavirus pandemic; and (xx) those additional factors discussed under Part I, Item 1A. Risk Factors in EXR’s and LSI’s respective Annual Reports on Form 10-K for the year ended December 31, 2022. Neither EXR nor LSI undertakes any duty to update any forward-looking statements appearing in this communication except as may be required by law.

Additional Information About the Proposed Transaction and Where to Find It

In connection with the proposed transaction, on May 23, 2023, EXR filed with the Securities and Exchange Commission (the “SEC”) a registration statement on Form S-4, which includes a document that serves as a prospectus of EXR and a joint proxy statement of EXR and LSI (the “joint proxy statement/prospectus”). Each party also plans to file other relevant documents with the SEC regarding the proposed transaction. The Form S-4 became effective on June 6, 2023. INVESTORS AND SECURITY HOLDERS ARE URGED TO READ THE JOINT PROXY STATEMENT/PROSPECTUS AND OTHER RELEVANT DOCUMENTS FILED WITH THE SEC WHEN THEY BECOME AVAILABLE, BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED TRANSACTION. EXR and LSI commenced mailing the definitive joint proxy statement/prospectus to stockholders on or about June 7, 2023. Investors and securityholders may obtain a free copy of the joint proxy statement/prospectus and other relevant documents filed by EXR and LSI with the SEC at the SEC’s website at www.sec.gov. Copies of the documents filed by EXR with the SEC are available free of charge on EXR’s website at www.extraspace.com or by contacting EXR’s Investor Relations at info@extraspace.com. Copies of the documents filed by LSI with the SEC are available free of charge on LSI’s website at www.lifestorage.com or by contacting LSI’s Investor Relations at (716) 633-1850 or bmaedl@lifestorage.com.

3

Participants in the Solicitation

EXR and LSI and their respective directors, executive officers and other members of management and employees may be deemed to be participants in the solicitation of proxies in respect of the proposed transaction. Information about directors and executive officers of EXR is available in the EXR proxy statement for its 2023 Annual Meeting, which was filed with the SEC on April 4, 2023. Information about directors and executive officers of LSI is available in the LSI proxy statement for its 2023 Annual Meeting, which was filed with the SEC on April 13, 2023. Other information regarding the participants in the proxy solicitation and a description of their direct and indirect interests, by security holdings or otherwise, will be contained in the joint proxy statement/prospectus and other relevant materials filed with the SEC regarding the proposed transaction. Investors should read the joint proxy statement/prospectus carefully before making any voting or investment decisions. Investors may obtain free copies of these documents from EXR and LSI as indicated above.

No Offer or Sale

This communication and the information contained herein shall not constitute an offer to sell or the solicitation of an offer to buy any securities, nor shall there be any sale of securities in any jurisdiction in which such offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such jurisdiction. No offering of securities shall be made except by means of a prospectus meeting the requirements of Section 10 of the Securities Act of 1933, as amended.

For more information, please visit www.extraspace.com.

4