DaBaba, you need an overnight Wilderness permit to camp overnight at Lone Pine Lake, the same permit required to camp at Trail Camp or other places on the Main Mt Whitney trail.
I think most people just go for it and try to get to their overnight camping spot in one push. But a few people do camp there.
Acclimating by car camping is easy if you head up to Horseshoe Meadows, off the Whitney Portal road, 45 minutes from Whitney Portal.
