You may be thinking about Fitz Lee. Rooney Lee had been seriously wounded at Brandy Station, just prior ti the Gettysburg Campaign.
By the afternoon of July 3rd, Stuart's men certainly were far from rested. All of them had been riding constantly and fighting frequently since June 26th. However, Confederate troopers should have benefited from a good night's sleep, so fatigue should not have been a factor at in the fields south of Gettysburg.
Custer's headlong charge leading the 7th Michigan Cavalry receives more attention than it should. After an earlier attack and repulse by both sides, Fitz Lee sent four regiments against the Federal horsemen. The 7th Michigan, a small and inexperienced regiment, formed the only Federal reserve available. Custer led it against Drake's 1st Virginia Cavalry, confidently riding forward. Custer's men pounded over dismounted troopers of the 9th Virginia Cavalry, but fire from the 13th Virginia Cavalry turned them to the left, away from the 1st Virginia Cavalry.
The unexpected change forced the Michiganders into a fence, breaking their charge. Most dismounted to engage in short-range combat with the 1st Virginia Cavalry, which had dismounted on the opposite side of the fence. The struggle was desperate and brief.
Leading that part of the regiment which had not been overthrown by the fence, Custer continued forward. Hampton's 1st North Carolina Cavalry and Jeff Davis Legion arrived to pounce upon the small band of Federals. Retreating as fast as they had come, Michigan troopers were also assailed by the 9th and 13th Virginia Cavalry, now remounted. Now hopelessly disordered, scattered survivors from the 7th Michigan streamed past the main Federal line, refusing all commands to halt. Only a vigorous counterattack by the 5th Michigan Cavalry maintained the main Federal line.
Longacre, The Cavalry at Gettusburg, pp 229-231.