MDAH has records listed as follows:
Hall, L.H., Surgeon, Field and Staff, (Sixty Day Troops) (Alcorn's Brigade)
Hall, L.H., Surgeon, Field and Staff, 9th Regt Miss Inf
Hall, Lemuel H, 1st LT,Co D,/Surgeon, Field and Staff, 1st Regt Miss Inf
Not sure about this group of 60 day troops, but the 9th Regt had 3 companies from Desoto Co, and Co D, of the 1st Regt was the Desoto Greys from Desoto Co., so in all likelyhood, they are all one in the same man.
As Jamie stated, ordering his service records would provide a clear timeframe of when he was in what unit.