Exhibit (a)(3)

July 11, 2012

Dear Lincare Stockholders:

We are pleased to report that Lincare Holdings Inc. (the “Company”) has entered into an Agreement and Plan of Merger, dated as of July 1, 2012 (the “Merger Agreement”), with Linde AG (“Parent”) and Linde US Inc. (“Purchaser” and together with Parent the “Offerors”), a wholly owned indirect subsidiary of Parent, which provides for the acquisition of the Company by Parent.

Pursuant to the Merger Agreement, the Offerors have commenced a tender offer (the “Offer”) today to purchase all of the issued and outstanding shares of the Company’s common stock, par value $0.01 per share (each, a “Share”) at a purchase price of $41.50 per Share (the “Offer Price”), subject to any required withholding of taxes, net to the seller in cash and without any interest thereon, on the terms and subject to the conditions provided for in the Offer to Purchase. The Offer is initially scheduled to expire at 12:00 midnight, New York City time, on Tuesday, August 7, 2012 (which is the end of day on August 7, 2012), subject to extension in certain circumstances as required or permitted by the Merger Agreement, the SEC or the NASDAQ Stock Market

The Merger Agreement provides, among other things, that after the completion of the Offer and the satisfaction or waiver of certain conditions, Purchaser will be merged with and into the Company, with the Company continuing as the surviving corporation (the “Merger”).

As set forth in the enclosed Solicitation/Recommendation Statement on Schedule 14D-9, after careful consideration, the Company’s board of directors has unanimously (i) approved the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger, upon the terms and subject to the conditions provided for in the Merger Agreement; (ii) determined that each of the Merger Agreement, the Merger and the Offer is advisable, fair to and in the best interests of the Company and its stockholders; and (iii) recommended that the Company’s stockholders accept the Offer and tender their Shares pursuant to the Offer and, if required by applicable law, vote in favor of the adoption of the Merger Agreement.

Accordingly, and for the other reasons described in more detail in the Solicitation/Recommendation Statement on Schedule 14D-9, the Company’s Board of Directors unanimously recommends that you accept the Offer and tender your Shares pursuant to the Offer and, if required, vote in favor of the adoption of the Merger Agreement.

In addition to the Solicitation/Recommendation Statement on Schedule 14D-9 that accompanies this letter, also enclosed is the Offerors’ Offer to Purchase and related materials, including a Letter of Transmittal for use in tendering your Shares. WE URGE YOU TO READ THE ENCLOSED OFFER TO PURCHASE, SOLICITATION/RECOMMENDATION STATEMENT ON SCHEDULE 14D-9 AND OTHER MATERIALS CAREFULLY.

We greatly appreciate and thank you for the continued support and encouragement you have shown the Company.

Sincerely,

John P. Byrnes

Chief Executive Officer