As you may know Maj. Lighfoot's Civil War career started when he enrolled in Co B, 2nd Reg't. Infantry Volunteers (3 month unit), enrolling in April 23, 1861 at age 26. He served honorably and was discharged July 30, 1861. This was a St. Louis unit. He is sometimes listed erroneously as having been with Co. B, 2nd MO Infantry -3 year unit.
He then joined the 12th MO Infantry in August 1861 summarized below:
Regimental History Twelfth Infantry MISSOURI (3-YEARS)
Twelfth Infantry. -- Cols., P. J. Osterhaus, Hugo Wangelin; Lieut-Cols., Otto Schadt, Jacob Karcher; Majs., Hugo Wangelin, Jacob Karcher, Gustavus Lightfoot, Fred Lederberger.
The regiment was organized in St. Louis in Aug 1861. Its first active service was as a part of Gen. Sigel's division in the Fremont expedition, moving successively to Jefferson City, Sedalia, Springfield, Wilson's Creek and Rolla, where it went into quarters.
Leaving Rolla in Jan., 1862, it marched with Gen. Curtis into Arkansas; fought at the battles of Pea Ridge, Leetown and Bentonville, pursuing the enemy from Pea Ridge through
southern Missouri and northern Arkansas to Batesville. On
Sept. 1, 1862, it left Helena and made an expedition to Ste. Genevieve and Pilot Knob.
Returning to Helena, it embarked on transports for the Yazoo River; fought at the battles of Chickasaw Bluffs and Arkansas Post; was then in the expedition through Yazoo pass; marched to Grand Gulf, where it joined Gen. Grant's army for the siege of Vicksburg, taking part in the various skirmishes and assaults incident to that movement...
Source: The Union Army, vol. 4, p. 262
More on the 12th and its make up may be in: (I've not read the article)
Hess, Earl J. "The 12th Missouri Infantry: A Socio-Military Profile of a Union Regiment." Missouri Historical Review, 76 (October 1981), pp. 53-77. or
Kircher, Henry A. A German in the Yankee Fatherland: The Civil War Letters of Henry A. Kircher. Edited by Earl J. Hess. Kent: Kent State University Press, 1983. [12th Missouri Volunteer Infantry]
The vast majority of Lightfoots were English in origin and the original lines go through Kentucky to Virginia. Both these units above were substantially German in makeup and with a name of Gustavus I would lean towards a German heritage versus an English one. There is a Lighfoot family line in Polk Co. Missouri during the war that is NOT related as best as I can tell.
Sgt E. Paul Reichhelm was German and from St. Louis how he is involved is a mystery at this stage.