<PAGE>   1
                                                                   EXHIBIT 10(k)

                [UNITED STATES LIME & MINERALS, INC. LETTERHEAD]

                               December 11, 1996

Mr. Robert K. Murray
United States Lime & Minerals, Inc.
12221 Merit Drive, Suite 500
Dallas, Texas 75251

Dear Bob:

         We appreciate your service to United States Lime & Minerals, Inc. and
its wholly owned subsidiaries (hereinafter "U.S. Lime"). This is to confirm our
discussions concerning the termination of your position, effective December 15,
1996, as Vice President - Operations for U.S. Lime, and U.S. Lime's offer and
your acceptance of this proposed Separation Agreement on the terms set forth
below.

         1.      SPECIAL SEPARATION BENEFITS. In consideration of your
continued services and the General Release and the Confidentiality of
Separation Agreement and Nondisparagement provisions of this Agreement, and
contingent upon your acceptance of the terms of this Agreement, U.S. Lime
offers you the following Special Separation Benefits:

         a.      Salary Continuation. U.S. Lime offers to continue to pay you
                 compensation in an amount equivalent to your regular monthly
                 salary for a period of six months from January 1, 1997 to June
                 30, 1997. You will be paid for the last two weeks of December
                 1996, from the vacation you have earned. These payments are
                 subject to all legal deductions and will be paid to you in
                 equal installments on regularly scheduled U.S. Lime paydays.

         b.      Fringe Benefits. For a period of six months from January 1,
                 1997 U.S. Lime offers to continue your current employee fringe
                 benefits with the exception of the company car and further
                 vacation accrual.  You will have the use of the company car
                 until January 15, 1997. During the salary continuation period,
                 you will be considered an employee for purposes of exercising
                 your option under the Company's 1992 Stock Option Plan.

         c.      Moving Costs. U.S. Lime will reimburse you for the reasonable
                 costs to move your household items and personal goods in an
                 amount not to exceed $6,000.
<PAGE>   2
         By execution of this Agreement, you acknowledge and agree that U.S.
Lime has no legal obligation to enter into such Separation Agreement with you.
You also acknowledge and agree that your acceptance of benefits pursuant to
such Separation Agreement and the attendant obligations as described in this
Agreement are in consideration of the promises and undertakings of U.S. Lime as
set forth in this Agreement. You further acknowledge and agree that should you
breach any of your obligations set forth in this Agreement (i) U.S. Lime will
have no obligation to make payments to you under this Agreement, but that all
other provisions of this Agreement shall remain in full force and effect, and
(ii) you may be required to repay any payments made to you and reimburse U.S.
Lime for any payments made on your behalf pursuant to this Agreement.

         2.      USE OF CONFIDENTIAL INFORMATION. You agree that all of the
documents and information to which you have had access during your employment
are confidential and may not be disseminated or disclosed by you to any other
parties, except as required by law or judicial process. In the event it appears
you will be compelled by law or judicial process to disclose such confidential
information, you should notify U.S. Lime in writing immediately upon your
receipt of a subpoena or other legal process to avoid potential liability.

         3.      GENERAL RELEASE. In consideration of the Special Separation
Benefits described above, you and your family members, heirs, successors, and
assigns (hereinafter collectively the "Releasing Parties") hereby release,
acquit, and forever discharge any and all claims and demands of whatever kind
or character, whether vicarious, derivative, or direct, that you or they,
individually, collectively, or otherwise, may have or assert against: (i) U.S.
Lime, (ii) any of U.S. Lime's subsidiaries or affiliated companies, or (iii)
any officer, director, stockholder, agent, employee, representative, attorney,
or any successor or assign of the entities just named (collectively the
"Released Parties"). This General Release includes but is not limited to any
claim or demand based on any state, federal, or local statutory or common law
that applies or is asserted to apply, directly or indirectly, to your
employment relationship or the termination of your employment relationship with
U.S. Lime, including but not limited to any claim for wrongful discharge,
unlawful discrimination on the basis of race, color, religion, sex, national
origin, age, citizenship status, disability, or any other form of
discrimination prohibited by jaw, retaliation, breach of contract (express or
implied), breach of any duty of good faith and fair dealing, violation of the
public policy of the United States, the State of Texas, or any other state,
tortious interference with contract or prospective contractual relations,
promissory estoppel, detrimental reliance, invasion of privacy, assault,
battery, conspiracy, intentional or negligent infliction of emotional distress,
defamation, duress, fraud or misrepresentation, loss of consortium, or any
other alleged negligent or intentional tort, or any violation of Title VII of
the Civil Rights Act of 1964, the Age Discrimination in Employment Act of 1967,
the Employee Retirement Income Security Act of 1974, the Americans with
Disabilities Act of 1990, the Family and Medical Leave Act, the Fair Labor
Standards Act, the Fair Credit Reporting Act, The Texas Workers' Compensation
Act or any other State or Federal statute, arising out of your employment
relationship or the termination of your employment relationship with U.S. Lime.
<PAGE>   3
         The effect of your acceptance of this Agreement is to waive, release,
and forever discharge any and all claims, demands, actions, or causes of action
of whatever kind or character that any of the Releasing Parties may now or
hereafter have against U.S. Lime or any of the other Released Parties for any
liability, whether vicarious, derivative, or direct, except for violations of
this Agreement. This includes, but is not limited to, any claims for damages
(actual or punitive), back wages, future wages, bonuses, reinstatement, accrued
vacation leave benefits, past and future employee benefits (except as to which
there is vested entitlement on June 30, 1997) including, but not limited to,
contributions to your employee benefit plans, compensatory damages, liquidated
damages, penalties, equitable relief, attorney's fees, costs of court,
interest, and any and all other loss, expense, or detriment of whatever kind
resulting from, growing out of, connected with, or related in any way to your
employment relationship or the termination of your employment relationship with
U.S. Lime. This general release does not apply to any rights or claims that may
arise as a result of violations of this Agreement.

         Should you or any of the other Releasing Parties violate this
Agreement, the Releasing Parties may be required to repay any payments made to
you or reimburse U.S. Lime for any payments made on your behalf pursuant to
this Separation Agreement. The Releasing Parties also may be held liable for
any of the Released Parties' damages caused by the violation, including without
limitation their costs and attorney's fees incurred in defending against such
action.

         4.      CONFIDENTIALITY OF SEPARATION AGREEMENT AND NON-DISPARAGEMENT.
In consideration of the Special Separation Benefits described above, you agree
that the terms of this Agreement shall be and remain confidential, and shall
not be disclosed by you to any party other than your spouse, attorney, and
accountant or tax return preparer if such persons have agreed to keep such
information confidential, and except as may be required by law or judicial
process. You further agree that, except as requested by U.S. Lime or as
compelled by law or judicial process, you will not institute or prosecute, or
cooperate in the institution of prosecution of, any proceeding or lawsuit
relating to the hiring, employment, or termination of employment of you or
others by U.S. Lime.

         You agree not to make any statement, oral or written, that directly or
indirectly impugns the quality or integrity of U.S. Lime's or any of the other
Released Parties' business practices, or make any other disparaging or
derogatory remarks about any of the Released Parties to any other parties. You
further agree and acknowledge that should you breach this obligation, you may
be required to repay any payments made to you or reimburse U.S. Lime for any
payments made on your behalf pursuant to this Agreement.

         5.      EXPIRATION OF OFFER. U.S. Lime's offer of this proposed
Separation Agreement will expire at midnight on the twenty-first day following
the date of this letter. You may accept this offer at any time before
expiration by executing this Agreement and returning it to the undersigned
representative of U.S. Lime.
<PAGE>   4
         6.      EFFECTIVE DATE. This Agreement will become effective and
enforceable seven days after you execute it ("Effective Date"). At any time
before the Effective Date of this Agreement, you may revoke your acceptance.
You also agree to re-execute this Agreement at any time on or after June 30,
1997 if U.S. Lime requests that you do so.

         7.      CONSULTATION WITH AN ATTORNEY. You have the right to consult
an attorney before executing this Agreement.

         8.      VOLUNTARY AGREEMENT. You acknowledge that your execution of
this Agreement is knowing and voluntary, that you have had a reasonable time to
deliberate regarding its terms, and that you have had the right to consult with
an attorney if you so desired.

                          -------------------------

         If you are in agreement with the foregoing provisions, please execute
the attached duplicate copy of this letter in the space provided below. This
letter shall then constitute a valid and binding agreement by and between U.S.
Lime and you, effective as of seven (7) days after the date of execution.

                                        Sincerely,

                                        UNITED STATES LIME & MINERALS, INC.

                                        By:       /s/ TIMOTHY W. BYRNE
                                            -----------------------------------

ACCEPTED AND AGREED TO:

/s/ ROBERT K. MURRAY
---------------------------------
ROBERT K. MURRAY

Date Signed: 12/12/96
             --------------------
<PAGE>   5

         I, Robert K. Murray, hereby resign as a Officer of United States Lime
& Minerals, Inc. In addition, I further resign as an Officer and Director from
Arkansas Lime Company, Corson Lime Company, Texas Lime Company and Colorado
Lime Company.

/s/ ROBERT K. MURRAY                                       12/12/96
-----------------------------------                --------------------------
Robert K. Murray                                              Date