Exhibit (a)(1)(E)

Offer To Purchase For Cash

All Outstanding Shares of Common Stock

of

LINCARE HOLDINGS INC.

at

$41.50 NET PER SHARE

Pursuant to the Offer to Purchase dated July 11, 2012 by

LINDE US INC.

a wholly owned indirect subsidiary of

LINDE AG

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON TUESDAY, AUGUST 7, 2012, UNLESS THE OFFER IS EXTENDED

July 11, 2012

To Our Clients:

Enclosed for your consideration are the Offer to Purchase, dated July 11, 2012 (the “Offer to Purchase”), and the related Letter of Transmittal in connection with the offer (the “Offer”) by Linde US Inc., a Delaware corporation (the “Purchaser”) and a wholly owned indirect subsidiary of Linde AG, a stock corporation organized under the laws of Germany, to purchase all the issued and outstanding shares of common stock, par value $0.01 per share (the “Shares”), of Lincare Holdings Inc., a Delaware corporation, at a price of $41.50 per Share, subject to any required withholding of taxes, net to the seller in cash and without any interest thereon, upon the terms and subject to the conditions of the Offer.

We or our nominees are the holder of record of Shares held for your account. A tender of such Shares can be made only by us as the holder of record and pursuant to your instructions. The Letter of Transmittal is furnished to you for your information only and cannot be used by you to tender Shares held by us for your account.

We request instructions as to whether you wish us to tender any or all the Shares held by us for your account, upon the terms and subject to the conditions set forth in the enclosed Offer to Purchase and the Letter of Transmittal.

Please note carefully the following:

1. The offer price for the Offer is $41.50 per Share, subject to any required withholding of taxes, net to you in cash and without any interest thereon, upon the terms and subject to the conditions of the Offer.

2. The Offer is being made for all the issued and outstanding Shares.

3. The Offer will expire at 12:00 midnight, New York City time, on Tuesday, August 7, 2012 (which is the end of the day on August 7, 2012), unless the Offer is extended by the Purchaser. Except as otherwise described in Section 4 of the Offer to Purchase, previously tendered Shares may be withdrawn at any time until the Offer has expired and, unless previously accepted for payment by the Purchaser pursuant to the Offer, may also be withdrawn at any time after September 8, 2012.

4. The Offer is subject to certain conditions described in Section 15 of the Offer to Purchase.

If you wish to have us tender any or all your Shares, please so instruct us by completing, executing, detaching and returning to us the Instruction Form on the detachable part hereof. An envelope to return your instructions to us is enclosed. If you authorize tender of your Shares, all such Shares will be tendered unless otherwise specified on the Instruction Form.

Your prompt action is requested. Your Instruction Form should be forwarded to us in ample time to permit us to submit the tender on your behalf before the Offer expires.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the laws of such jurisdiction. In any jurisdiction where the securities, blue sky or other laws require the Offer to be made by a licensed broker or dealer, the Offer shall be deemed to be made on behalf of the Purchaser by Morgan Stanley & Co. LLC, which is acting as the Dealer Manager for the Offer, or by one or more registered brokers or dealers that are licensed under the laws of such jurisdiction.

2

INSTRUCTION FORM

With Respect to the Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

LINCARE HOLDINGS INC.

at

$41.50 NET PER SHARE

Pursuant to the Offer to Purchase

dated July 11, 2012

by

LINDE US INC.

a wholly owned indirect subsidiary of

LINDE AG

The undersigned acknowledge(s) receipt of your letter and the enclosed Offer to Purchase, dated July 11, 2012, and the related Letter of Transmittal, in connection with the offer (the “Offer”) by Linde US Inc., a Delaware corporation (the “Purchaser”) and a wholly owned indirect subsidiary of Linde AG, a stock corporation organized under the laws of Germany, to purchase all the issued and outstanding shares of common stock, par value $0.01 per share (the “Shares”), of Lincare Holdings Inc., a Delaware corporation, at a price of $41.50 per Share, subject to any required withholding of taxes, net to the seller in cash and without any interest thereon, upon the terms and subject to the conditions of the Offer.

The undersigned hereby instruct(s) you to tender to the Purchaser the number of Shares indicated below or, if no number is indicated, all Shares held by you for the account of the undersigned, upon the terms and subject to the conditions set forth in the Offer.

ACCOUNT NUMBER:                     

NUMBER OF SHARES BEING TENDERED HEREBY:                     SHARES*

The method of delivery of this document is at the election and risk of the undersigned. If delivery is by mail, then registered mail with return receipt requested, properly insured, is recommended. In all cases, sufficient time should be allowed to ensure timely delivery.

* Unless otherwise indicated, it will be assumed that all Shares held by you for the account of the undersigned are to be tendered.

Dated:                     

(Signature(s))

Please Print Name(s)

Address                                                                                                                                                                        

Include Zip Code

Area Code and

Telephone No.                             

Taxpayer Identification

or Social Security No.