Oooops!
This may have been what you are referring to:
Name: L H Parham
Enlistment Date: 1864
Military Unit: Personal Papers Fold.3
There are two files, one under L. A. Parham, and the other L. H. Parham
https://www.fold3.com/image/268698158?terms=Parham,%20L
https://www.fold3.com/image/268698158
https://www.fold3.com/image/268698168
Military Unit:
Personal Papers
Compiled Service Records of Volunteer Union Soldiers Who Served in Organizations from the State of Tennessee