Good morning,
I did a little scratching around and found Corporal Lorenzo Hart in L Company of the 1st Michigan Cavalry.

The website Michiganinthewar.org lists Lorenzo as mustering into Company L of the 1st MI Cavalry at the age of 20. It also lists Lorenzo Hart in the roster of Michigan deaths with the following:

Hart, Lorenzo 1st Cavalry, Company L Grand Rapids Mar 30, 1865

March 30th was two days before the Battle of Five Forks so it’s very possible he was killed or mortally wounded in the preparation operations that Sheridan's Cavalry Corps was running at the time. As for the "Tin Willy Company" I can only speculate that this was a nick-name for Company L. Flamboyant or funny names for companies were not uncommon for either side during the Civil War and were often points of pride for the troops in them. I hope this is helpful!