Lorenzo subsequently returned to the regiment, was wounded and captured at Vicksburg July 4, 1863.
Note, this was not Needham.
It's somewhat of a mystery why Lorenzo was at Lauderdale at this time when the regiment was operating much to the North. Perhaps, he, and perhaps his brother were going to or returning on furlough from home in the Shubuta area. This could also explain how the regiment later obtained the intelligence that Needham had died in hospital.
Unfortunately there survived no patient book for the Lauderdale Hospital. The National Archives hold a Prescription book, 1862-3, hopefully this might list patients. An Order book for 1862-1864 is in the Minnesota Historical Society holdings. I have no idea what would be found in an Order book.
I will be in the Washington, D.C. area in a little over two weeks from now. I'll see what I can find when I visit the National Archives.