<PAGE>   1
                                                                    EXHIBIT 10.8


             SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT


         THIS SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT (the
"Amendment"), dated as of January 25, 2000, is among LENNOX INTERNATIONAL INC.,
a Delaware corporation ("Borrower"); each of the lenders listed as a lender on
the signatures pages hereto (individually, a "Lender" and, collectively, the
"Lenders"), CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking
association, as administrative agent for the Lenders (in such capacity, the
"Administrative Agent"), WACHOVIA BANK, N.A., a national banking association, as
syndication agent (in such capacity, the "Syndication Agent" and together with
the Administrative Agent, herein the "Agents") and THE BANK OF NOVA SCOTIA, as
documentation agent.

         Borrower, the Agents and the Lenders, have entered into that certain
Revolving Credit Facility Agreement dated as of July 29, 1999 (as amended by the
First Amendment to Revolving Credit Facility Agreement dated as of August 6,
1999, the "Credit Agreement"). Borrower, the Lenders and the Agents desire to
amend the Credit Agreement as herein set forth.

         NOW, THEREFORE, in consideration of the premises herein contained and
other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, the parties hereto agree as follows effective as of the
date hereof:

                                    ARTICLE 1

                                   Definitions

         Section 1.1 Definitions. Capitalized terms used in this Amendment and
defined in the Credit Agreement, to the extent not otherwise defined herein,
shall have the same meaning as in the Credit Agreement, as amended hereby.

                                    ARTICLE 2

                                   Amendments

         Section 2.1. Amendment to Section 2.06. The chart in Section 2.06(d) is
amended in its entirety to read as follows:


<TABLE>
<CAPTION>
=========================================================================================
                                                                           Commitment Fee
Debt to Adjusted EBITDA Ratio                                     Margin   Percentage
=========================================================================================
<S>                                                             <C>        <C>
Greater than 3.0 to 1.0                                           1.250%     0.300%
-----------------------------------------------------------------------------------------
Greater than 2.5 to 1.0 but less than or equal to 3.0 to 1.0      1.125%     0.300%
-----------------------------------------------------------------------------------------
Greater than 2.0 to 1.0 but less than or equal to 2.5 to 1.0      0.875%     0.250%
-----------------------------------------------------------------------------------------
Greater than 1.5 to 1.0 but less than or equal to 2.0 to 1.0      0.750%     0.200%
-----------------------------------------------------------------------------------------
Greater than 1.0 to 1.0 but less than or equal to 1.5 to 1.0      0.625%     0.1875%
-----------------------------------------------------------------------------------------
Less than or equal to 1.0 to 1.0                                  0.500%     0.150%
=========================================================================================
</TABLE>

         Section 2.2 Amendment to Section 5.15. Clause (b) in Section 5.15 of
the Credit Agreement is amended in its entirety to read as follows:

SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT, Page 1

<PAGE>   2


                  (b) Consolidated Indebtedness to Adjusted EBITDA. As of the
         last day of each fiscal quarter during the periods described below, the
         Borrower shall not permit the ratio of Consolidated Indebtedness
         outstanding as of such day to the Adjusted EBITDA for the four (4)
         fiscal quarters then ended to exceed: (i) 3.00 to 1.00 at all times
         other than as described in the following clause (ii); or (ii) 3.25 to
         1.00 for all fiscal quarters ending prior to March 31, 2001 if, and
         only if prior to any such fiscal quarter end Borrower shall have
         delivered to the Administrative Agent evidence satisfactory to it that
         the holders of the Indebtedness outstanding under the Senior Note
         Purchase Agreements and the holders of any other Indebtedness that have
         the benefit of a Consolidated Indebtedness to Adjusted EBITDA ratio the
         same or similar to this Section 5.15(b), shall have agreed to a maximum
         ratio not to exceed 3.25 to 1.00 for all fiscal quarters prior to March
         31, 2001.

                                    ARTICLE 3

                                  Miscellaneous

         Section 3.1 Ratifications. The terms and provisions set forth in this
Amendment shall modify and supersede all inconsistent terms and provisions set
forth in the Credit Agreement and except as expressly modified and superseded by
this Amendment, the terms and provisions of the Credit Agreement are ratified
and confirmed and shall continue in full force and effect. Borrower, the Agents,
and the Lenders agree that the Credit Agreement as amended hereby shall continue
to be legal, valid, binding and enforceable in accordance with its terms.

         Section 3.2 Fees and Expenses. In accordance with the terms of Section
8.05 of the Credit Agreement, Borrower agrees to pay all costs and expenses
incurred by either Agent in connection with the preparation, negotiation and
execution of this Amendment, including, without limitation, the costs and fees
of legal counsel.

         Section 3.3 Applicable Law. THIS AMENDMENT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS.

         Section 3.4 Successors and Assigns. This Amendment is binding upon and
shall inure to the benefit of the Agents, the Lenders and Borrower and their
respective successors and assigns.

         Section 3.5 Counterparts. This Amendment may be executed in one or more
counterparts and on telecopy counterparts, each of which when so executed shall
be deemed to be an original, but all of which when taken together shall
constitute one and the same agreement.

         Section 3.6 Headings. The headings, captions, and arrangements used in
this Amendment are for convenience only and shall not affect the interpretation
of this Amendment.

         Section 3.7 ENTIRE AGREEMENT. THIS AMENDMENT EMBODIES THE FINAL, ENTIRE
AGREEMENT AMONG THE PARTIES HERETO AND SUPERSEDES ANY AND ALL PRIOR COMMITMENTS,
AGREEMENTS, REPRESENTATIONS AND UNDERSTANDINGS, WHETHER WRITTEN OR ORAL,
RELATING TO THIS AMENDMENT, AND MAY NOT BE CONTRADICTED OR VARIED BY EVIDENCE OF
PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OR DISCUSSION OF THE
PARTIES HERETO. THERE ARE NO ORAL AGREEMENTS AMONG THE PARTIES HERETO.


SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT, Page 2

<PAGE>   3

         Executed as of the date first written above.

                                   LENNOX INTERNATIONAL INC.


                                   By:    /s/ Clyde Wyant
                                          --------------------------------------
                                          Clyde Wyant
                                          Executive Vice President,
                                          Chief Financial Officer

                                   CHASE BANK OF TEXAS,
                                   NATIONAL ASSOCIATION,
                                   individually as Lender and as
                                   Administrative Agent


                                   By:    /s/ Allen King
                                          --------------------------------------
                                          Allen King
                                          Vice President

                                   WACHOVIA BANK, N.A., individually as a
                                   Lender and as Syndication Agent


                                   By:    /s/ A. Michael Klein
                                          --------------------------------------
                                          Name: A. Michael Klein
                                          Title: Vice President

                                   THE BANK OF NOVA SCOTIA,
                                   individually as a Lender and as
                                   documentation agent


                                   By:    /s/ F.C.H. Ashby
                                          --------------------------------------
                                          Name: F.C.H. Ashby
                                          Title: Senior Manager Loan Operations

                                   THE NORTHERN TRUST COMPANY,
                                   individually as a lender and as a co-agent


                                   By:    /s/ Jaron Grimm
                                          --------------------------------------
                                          Name: Jaron Grimm
                                          Title: Vice President


SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT, Page 3

<PAGE>   4

                                   BANK ONE, TEXAS, N.A., as a Lender


                                   By:    /s/ Gina A. Norris
                                          --------------------------------------
                                          Name: Gina A. Norris
                                          Title: Managing Director

                                   BANK OF TEXAS, N.A., as a Lender


                                   By:    /s/ David Broussard, Jr.
                                          --------------------------------------
                                          Name: David Broussard, Jr.
                                          Title: SVP

                                   THE BANK OF TOKYO-MITSUBISHI,
                                   LTD., as a Lender


                                   By:    /s/ D. Barnell      /s/ John M. Mearns
                                          --------------------------------------
                                          Name: D. Barnell        John M. Mearns
                                          Title: Vice President     VP & Manager

                                   WELLS FARGO BANK (TEXAS), N.A.,
                                   as a Lender


                                   By:    /s/ Juan J. Sanchez
                                          --------------------------------------
                                          Name: Juan J. Sanchez
                                          Title: AVP

                                   ROYAL BANK OF CANADA,
                                   as a Lender


                                   By:    /s/ N.G. Millar
                                          --------------------------------------
                                          Name: N.G. Millar
                                          Title: Senior Manager

                                   ABN AMRO BANK N.A., as a Lender


                                   By:    /s/ Jamie A. Conn
                                          --------------------------------------
                                          Name: Jamie Conn
                                          Title: Vice President


                                   By:    /s/ Eric R. Hollingsworth
                                          --------------------------------------
                                          Name: Eric R. Hollingsworth
                                          Title: Vice President


SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT, Page 4

<PAGE>   5

                                   THE BANK OF NEW YORK, as a Lender


                                   By:    /s/ Mark T. Familo
                                          --------------------------------------
                                          Name: Mark T. Familo
                                          Title: Vice President

                                   COMPASS BANK, as a Lender


                                   By:    /s/ Paul Howell
                                          --------------------------------------
                                          Name: Paul Howell
                                          Title: Assistant V.P.


SECOND AMENDMENT TO REVOLVING CREDIT FACILITY AGREEMENT, Page 5