UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM 4
STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP

[   ] Check this box if no longer subject to Section 16. Form 4 or Form 5
    obligations may continue.
1. Name and Address of Reporting Person(s)
   Alvarado, Linda G.
   2140 Lake Park Blvd.
   Richardson,  Texas  75080-2254
2. Issuer Name and Ticker or Trading Symbol
   Lennox International Inc. (LII)
3. I.R.S. Identification Number of Reporting Person, if an entity (Voluntary)
4. Statement for Month/Year
   5/02
5. If Amendment, Date of Original (Month/Year)
6. Relationship of Reporting Person(s) to Issuer (Check all applicable)
   [X] Director                   [ ] 10% Owner
   [ ] Officer (give title below) [ ] Other (specify below)
7. Individual or Joint/Group Filing (Check Applicable Line)
   [X] Form filed by One Reporting Person
   [ ] Form filed by More than One Reporting Person



Table I   Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
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1)Title of Security          2)Trans-    3.Trans-   4.Securities Acquired(A)    5)Amount of    6. Ownership    7)Nature of
                             action      action     or Disposed of (D)          Securities     Form: Direct    Indirect
                             Date        Code                  A                Beneficially   (D) or          Beneficial
                             (Month/                           or               Owned at       Indirect        Ownership
                             Day/Year)   Code V     Amount     D    Price       End of Month   (I)
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                                       1



Table II (PART 1) Derivative Securities Acquired, Disposed of, or Beneficially
Owned (Columns 1 through 6)
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1)Title of Derivative          2)Conversion    3)Trans-       4)Trans-  5)Number of Derivative     6)Date Exercisable and
Security                       or Exercise     action         action    Securities Acquired (A)    Expiration Date
                               Price of        Date           Code      or Disposed of (D)
                               Derivative
                               Security                       Code  V   A                D         Date Exercisable  Expiration Date
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Non-Qualified Stock Option     $16.3650        5/20/02        A     V   11,348                     (1)               12/14/08
(right to purchase




Table II (PART 2) Derivative Securities Acquired, Disposed of, or Beneficially
Owned (Columns 1,3 and 7 through 11)
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1)Title of Derivative          3)Trans-  7)Title and Amount                  8)Price       9)Number of   10)Ownership   11)Nature of
Security                       action    of Underlying                       of Deri-      Derivative    Form of        Indirect
                               Date      Securities                          vative        Securities    Derivative     Beneficial
                                                               Amount or     Security      Beneficially  Security: or   Ownership
                                                               Number of                   Owned at      Direct (D) or
                                         Title                 Shares                      End of Month  Indirect (I)
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Non-Qualified Stock Option     5/20/02   Common Stock, par
(right to purchase                       value $.01 per share  11,348                      11,348        D



Explanation of Responses:

(1)  The option becomes exercisable in three equal annual installments, commencing one year after the date of grant.
- Attorney-in-fact pursuant to the power of attorney dated 7/9/99.



SIGNATURE OF REPORTING PERSON
/S/ By: Carl E. Edwards, Jr.
    For: Linda G. Alvarado
DATE 6/7/02