Have we discussed Lorenzo who must have been kin?

Odds are that Needham was at the Lauderdale hospital at the same time.

Lorenzo Temples, Private, Company E, 37th Mississippi Infantry, present on August 30, 1862, recorded as at the General Hospital, Lauderdale Springs, Miss. sometime in September, 1862, recorded as sick in hospital on the October 30, 1862 muster roll, and as absent, in hospital at the end of year muster, returning back to the company sometime in January/February, 1864

M269: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi

A prescription book for the Lauderdale Springs General Hospital, for the period 1862-63 is located at the National Archives in Record Group 109, (ch. VI, vol. 643, p. 1-60)

It's a long shot, but might be worth the effort if you could find someone in the DC area to investigate.