This may be him on this list: 7th Tennessee Cavalry Roster USA (Union) Company A

http://www.tngenweb.org/benton/7throster.html

Lawler, John A. Private
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John Abner Lawler--5/14/1845--4/14/1922--Atwood Cemetery, Carroll Co, TN

http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GScid=2320741&GRid=41301827&
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John A. Lawler filed for pension in TN 7/28/1893..You can order his records from this website..See the enclosed Red Box top of the board..
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Gay