AMENDMENT AND WAIVER TO MANAGEMENT STOCKHOLDERS AGREEMENT

Exhibit 4.1

AMENDMENT AND WAIVER TO

MANAGEMENT STOCKHOLDERS’ AGREEMENT

This Amendment and Waiver Agreement (this “Amendment”) is entered into as of May 31, 2012 by and between LPL Investment Holdings Inc. (the “Company”) and Robert J. Moore.

WHEREAS, on November 23, 2010, the Company entered into a Management Stockholders’ Agreement with Stephanie L. Brown, Mark S. Casady, William E. Dwyer III, Robert J. Moore and Esther M. Stearns (the “Agreement”) setting forth, among other things, certain transfer restrictions;

WHEREAS, in accordance with Section 4.02 of the Agreement, the Company and Robert J. Moore wish to amend the Agreement to remove Mr. Moore as a party thereto and waive the restrictions and obligations of the Agreement with respect to Mr. Moore;

NOW, THEREFORE, the parties hereto hereby agree as follows:

1. Amendment and Waiver. The Agreement is hereby amended to remove Robert J. Moore as a party thereto. The Company hereby waives all restrictions and obligations contained in the Agreement as they pertain to Robert J. Moore, including the transfer restrictions set forth in Section 2.01 of the Agreement.

2. Miscellaneous.

2.01 Severability. If any provision of this Amendment shall be declared by any court of competent jurisdiction to be illegal, void or unenforceable, all other provisions of this Agreement, to the extent permitted by law, shall not be affected and shall remain in full force and effect. Upon any such determination, the parties shall negotiate in good faith in an effort to agree upon a suitable and equitable substitute provision to effect the original intent of the parties.

2.02 Entire Agreement. Except as otherwise expressly set forth herein, the Agreement, as modified by this Amendment, embodies the complete agreement and understanding among the parties hereto with respect to the subject matter hereof and supersedes and preempts any prior understandings, agreements or representations by or among the parties, written or oral, that may have related to the subject matter hereof in any way.

2.03 Counterparts. This Amendment may be executed in separate counterparts each of which shall be an original and all of which taken together shall constitute one and the same agreement.

2.04 Governing Law; Consent to Jurisdiction.

(a) This Amendment shall be governed by and construed in accordance with the laws of the State of Delaware. The parties hereto agree that any suit, action or proceeding (“Litigation”) seeking to enforce any provision of, or based on any matter arising out of or in connection with, the Agreement or this Amendment or the transactions

contemplated thereby or hereby shall be brought in any federal court located in the State of Delaware or any Delaware state court. Each of the parties hereto hereby irrevocably and unconditionally waives, and agrees not to assert, by way of motion, as a defense, counterclaim or otherwise, in any such Litigation, the defense of sovereign immunity, any claim that it is not personally subject to the jurisdiction of the aforesaid courts for any reason, other than the failure to serve process in accordance with this Section 2.04, that it or its property is exempt or immune from jurisdiction of any such court or from any legal process commenced in such courts (whether through service of notice, attachment prior to judgment, attachment in aid of execution of judgment, execution of judgment or otherwise), and to the fullest extent permitted by applicable law, that the Litigation in any such court is brought in an inconvenient forum, that the venue of such Litigation is improper, or that this Amendment, or the subject matter hereof, may not be enforced in or by such particular courts and further irrevocably waives, to the fullest extent permitted by applicable law, the benefit of any defense that would hinder, fetter or delay the levy, execution or collection of any amount to which the party is entitled pursuant to the final judgment of any court having jurisdiction. Each of the parties irrevocably and unconditionally waives, to the fullest extent permitted by applicable law, any and all rights to trial by jury in connection with any Litigation arising out of or relating to the Agreement or this Amendment or the transactions contemplated thereby or hereby.

(b) Each of the parties hereto irrevocably consents to the service of process out of any of the aforementioned courts in any such Litigation by the mailing of copies thereof by registered mail, postage prepaid, to such party at its address set forth in the Agreement, such service of process to be effective upon acknowledgment of receipt of such registered mail.

(c) The parties hereto each expressly acknowledge that the foregoing waivers are intended to be irrevocable under the laws of the State of Delaware and of the United States of America; provided that consent by the parties hereto to jurisdiction and service contained in this Section 2.04 solely for the purpose referred to in this Section 2.04 and shall not be deemed to be a general submission to said courts or in the State of Delaware other than for such purpose.

2.05 Interpretation. The headings contained in this Amendment are for reference purposes only and shall not affect in any way the meaning or interpretation of this Amendment or the Agreement.

2.06 Effect of Amendment. This Amendment modifies only the obligations of the parties hereto and shall not be considered a modification of the rights of any other Executive (as defined in the Agreement) party to the Agreement. In the event of any conflict or inconsistency between the terms of this Amendment and the terms of the Agreement, the terms of this Amendment will control. Except to the extent expressly modified herein or in conflict with the terms of this Amendment, the terms of the Agreement shall remain in full force and effect.

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IN WITNESS WHEREOF, the undersigned have executed this Amendment and Waiver Agreement as of the date first above written.

[Signature Page to Amendment and Waiver Agreement]