LQ MANAGEMENT L.L.C. 909 HiddenRidge, Suite 600 Irving, Texas 75038 January 7, 2013

Exhibit 10.7

LQ MANAGEMENT L.L.C.

909 Hidden Ridge, Suite 600

Irving, Texas 75038

January 7, 2013

Mr. Keith Cline

c/o LQ Management L.L.C.

909 Hidden Ridge, Suite 600

Irving, Texas 75038

    Re:      Terms of Severance Arrangement

Dear Mr. Cline:

This letter agreement sets forth the terms of the severance you will be entitled to receive in the event your employment with LQ Management L.L.C. (the “Company”) is terminated by the Company other than for Cause (as defined herein) and other than pursuant to the transfer of your employment to an affiliate of the Company that assumes the Company’s obligations under this letter agreement.

If the Company terminates your employment with the Company other than for Cause, and other than pursuant to the transfer of your employment to an affiliate of the Company that assumes the Company’s obligations under this letter agreement, you will be entitled to receive a severance amount equal to the amount, if any, by which $2,400,000 exceeds the total value of your long-term incentive plan participation (with the “total value” thereof meaning the value of the plan at the time of termination of your employment plus any prior distributions under the plan). This means that if your long-term incentive plan has a total value (as so determined) of at least $2,400,000 at the time of your termination, you would not be entitled to any severance payment in connection with your termination. For purposes hereof, your long-term incentive plan participation means the interest you own as a Class B-2 Member in LQ Services L.L.C. pursuant to the terms of the LQ Services L.L.C. Amended and Restated Limited Liability Company Agreement, as amended (including, without limitation, the Third Amendment thereto that created the Class B-2 Units held by you, and any prior and future amendments thereto) and the distributions you may receive from time to time by virtue of your ownership of that interest. For the avoidance of doubt, if you terminate your employment with the Company for any reason (including your death or disability), you will not be entitled to any severance amount.

As used in this letter agreement, the term “Cause” means that, prior to any termination of your employment, you shall have committed: (i) an act of willful misconduct, fraud, embezzlement, theft, or any other act constituting a felony, involving moral turpitude or causing material harm, financial or otherwise, to the Company; (ii) a demonstrably intentional and deliberate act or failure to act, including gross neglect in duties, (other than as a result of incapacity due to physical or mental illness), which is committed by you in bad faith, which causes or can be expected to cause material financial injury to the Company; or (iii) an intentional and material breach of your responsibilities that you fail to cure within 30 days after written notice from the President and Chief Executive Officer of the Company specifying the breach and requesting a cure. For purposes of this paragraph, no act, or failure to act, on your

part shall be deemed “intentional” if it was due primarily to an error in judgment or negligence, but shall be deemed “intentional” only if done, or omitted to be done, by you not in good faith and without reasonable belief that your action or omission was in, or not opposed to, the best interest of the Company.

If your employment with the Company is terminated by the Company under circumstances in which you would be entitled to receive a severance amount in accordance with the terms of this letter agreement as a result of such termination, the applicable severance amount will be paid to you in a lump sum within 60 days following your termination of employment, but contingent on your execution and effectiveness of a general release of claims against the Company and its affiliates in the Company’s standard form for departing executives eligible for severance.

Please indicate your agreement to the terms and conditions of this letter agreement by signing the enclosed copy of this letter agreement in the space indicated below and returning it to the undersigned. This letter agreement may be executed in counterparts, each of which shall constitute an original and all of which, taken together, shall constitute one and the same agreement.

Accepted and agreed as of the date

set forth above.