I cannot prove who the man was, but looking through some records of the 5th Iowa Cavalry on the Internet and assuming that the man has been noted as a Lieut. in the 5th Iowa Cavalry is true, I found 2 Lieuts that died in mid 1862.
Michael Gallagher: b. 1838 Ireland, son of Hugh Gallagher and Catherine McCallum, KIA by gunshot the 6th or 7th of Nov 1862 at the Battle of Garrettsburg, Christian Co., KY, and buried at the Ft. Donelson National Cemetery in grave 64.
Milton Sanford Summers was mortally wounded 27 August 1862 at Cumberland Iron Works

If the 2 sons were killed in the fall of 1862, Gallagher seems suspect.
Maybe someone with availability to military records could find more about Gallagher to confirm or eliminate him from the murderous deed.