LOCK-UP AGREEMENT

EXHIBIT 10.4

LOCK-UP AGREEMENT

January 31, 2003

Dorchester Minerals, Ltd.

3738 Oak Lawn Avenue

Dallas, Texas 75219

Ladies and Gentlemen:

The undersigned understands that Dorchester Minerals, L.P. (the “Partnership”), has entered into a Combination Agreement, dated December 13, 2001 (the “Combination Agreement”), with various parties providing, among other things, for the public offering (the “Public Offering”) by the Partnership of common units of limited partnership interest (the “Securities”) of the Partnership pursuant to the Partnership’s joint Registration Statement, Proxy Statement and Prospectus on Form S-4 filed with the Securities and Exchange Commission on May 15, 2002, as amended, and which was declared effective on October 30, 2002 (the “Registration Statement”). Capitalized terms used and not otherwise defined herein have the meaning ascribed to them in the Combination Agreement.

In consideration of the Partnership’s agreement to make the Public Offering of the Securities, and for other good and valuable consideration, receipt and sufficiency of which is hereby acknowledged, the undersigned hereby agrees, from the date hereof until the second anniversary of the Closing of the Combination, not to offer to sell, contract to sell or otherwise sell, dispose of, loan, pledge, encumber, transfer or grant any rights with respect to or interest in (including any option to buy or sell) (collectively, a “Disposition”) any of the Securities owned by the undersigned directly at the time of execution of this agreement or with respect to which the undersigned has an economic interest (collectively, “Covered Securities”). This lock-up agreement shall expire as to 25% of the initial amount of the Covered Securities upon each of the second, third and fourth anniversaries of the Closing of the Combination, such that following the fourth anniversary of the Closing of the Combination, the undersigned is permitted to sell up to 75% of the initial amount of the Covered Securities, which restriction shall continue until such time as the undersigned ceases to be a manager of Management GP. In no event shall this lock-up agreement cover Securities which the undersigned beneficially owns, or is deemed to beneficially own, but in which he does not have an economic interest. Limited partnerships in existence on the date of this lock-up agreement and in which the undersigned has an economic interest solely as a limited partner which, in the aggregate, represents less than 5% of the Covered Securities shall not be prohibited from making a Disposition with respect to any or all of the Covered Securities owned by the limited partnership. A partnership or entity of which the undersigned is an officer or general partner shall not be prohibited from making an in-kind distribution of Covered Securities to its owners, provided that any Covered Securities distributed to the undersigned, or a partnership or entity of which the undersigned is a general partner or officer, will be subject to the provisions of this lock-up agreement. The prohibition on a Disposition of Covered Securities will be subject to exceptions for (i) bona fide gifts and charitable contributions of up to a total of 25,000 common units during the first two years of this lock-up agreement and (ii) transfers to members of the undersigned’s immediate family, or a trust or

trusts for the benefit of any of such family members, provided that such family member or trust agrees in writing to be subject to the provisions of this lock-up agreement.

The foregoing restrictions are expressly agreed to preclude the undersigned holder of Covered Securities from:

(a) engaging in any hedging or other transaction which is designed to or reasonably expected to lead to or result in a Disposition of Covered Securities during the during the term of this lock-up agreement even if such Covered Securities would be disposed of by someone other than the undersigned. Such prohibited hedging or other transactions would include without limitation any short sale (whether or not against the box) or any purchase, sale or grant of any right (including without limitation any put or call option) with respect to any Covered Securities or with respect to any security (other than a broad-based market basket or index) that includes, relates to or derives any significant part of its value from Covered Securities.

(b) filing with the SEC a registration statement relating to, requesting the registration of, or publicly disclosing the intention to make any such request or filing of the offer or sale of Covered Securities, as to any Covered Securities that are subject to the terms of this lock-up agreement at the time of such filing, request or disclosure.

The undersigned understands that the Partnership will rely upon the representations set forth in this lock-up agreement in proceeding with the Public Offering. The undersigned confirms that this lock-up agreement is irrevocable and shall be binding upon the undersigned’s heirs, legal representatives, successors and assigns. Furthermore, the undersigned hereby agrees and consents to the entry of stop transfer instructions with the Partnership’s transfer agent against the transfer of the Covered Securities held by the undersigned except in compliance with this lock-up agreement.

Accepted as of the date first set forth above:

Dorchester Minerals, L.P.

By:    Dorchester Minerals Management LLC, General Partner

By:    /s/    James E. Raley                        

(authorized signatory)