I found a James J. Lister, Sgt, Co D, 35th Ill US Infantry. His records lists the following characteristics:
Residence: Higginsville, Vermilion Co, Il
Age: 39 Height: 5'9 Hair: Dark Eyes: Blue Comp: Fair
Marital Status: Married Occupation: Farmer Nativity: Ross County, OH
Joined when: July 3, 1861 Joined where: Higginsville, IL
Joined by Whom: Cpt Timmons Period: 3 years Muster In: Aug 28, 1861 Muster in Where: St Louis, MO
Remarks: Promoted to 1SGT killed in action at Chickamauga Sep 19, 1863
Can this man be the one you are looking for? I have not found his name in the VA National Grave Locator, but I am still looking.
The John Lister of the 96th Ill, Co F, was mustered out in 1865.