i LOVE sleeping in my car at the Cottonwood Pass (not Lakes) trailhead. It is soooo quiet and peaceful. just drive to the end of Horseshoe Meadow Road and park. no slamming doors at 2am, no bears lumbering around. just lots of stars in the sky, a bathroom, water spigot, and some low backpacker bear lockers that always have room.
i never bother getting a campsite so i don't know the availability, but i always look forward to a great night of sleep up there in my car.
p.s. if you have time for a warm-up hike, the hike from the TH to Trail Peak which is the bald peak SW of the TH is a great little hike to help acclimate you.