It doesn't look like he died in the Battle for Lookout Mountain if the Indiana Adjutant General's records are correct. The battle on Lookout Mountain occurred in November 1863 so according to these records he wasn't in the army yet.

This is the information that the Report of the Adjutant General of the State of Indiana had for him:

Volume V Page 21

Indiana Volunteers

Thirtieth Regiment Infantry-Re-Organized.

Private: Allman, John Residence: Columbus Date of Muster: Oct 14, ’64 Remarks: Died, Nashville, May 24, ‘65

Volume VIII Page 495 in a listing of deceased soldiers

Thirtieth Regiment Infantry-Re-Organized.
Three Years Service

Name: Allman, John Rank: Private Company: A Cause: Disease Place: Nashville Date of Death: May 24, ‘65 Where Buried: Not reported

I checked both the Sons of Union Veterans of the Civil War Grave Registration site at http://www.suvcwdb.org/home/ and the VA’s National Gravesite Locator at http://gravelocator.cem.va.gov/j2ee/servlet/NGL_v1 . He was not listed at either site.

You might want to order his service records. You can get a copy of card file from the Index to Muster Rolls from the Indiana State Archives for a low price. You could also order his Compiled Military Service Record (CMSR) from the National Archives at http://www.archives.gov/genealogy/military/civil-war/ . It contains more information but it is more expensive and there is no guarantee that it will list his burial site.