There was no Lee with the given name starting with the letter 'A' in the 2nd Va Cav.

James E. Lee

Residence was not listed;
Enlisted on 8/25/1864 at Appomattox County, VA as a Private.
On 8/25/1864 he mustered into "H" Co. VA 2nd Cavalry
He was Killed on 10/9/1864 at Tom's Brook, VA
American CW Research Database

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James E. Lee, Private, Company H, 2nd Virginia Cavalry, enlisted August 25, 1864 at Appomattox Court House by Lt Fentress for the duration of the war, "Killed 8 Oct. 1864"

M324" Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Virginia