Try camping the night before at either Whitney Portal or Horseshoe Meadows.....This is better than staying in Lone Pine at roughly 4k feet.
light hiking the day before is good acclimation. many people do not sleep well up at the portals - especially when you are not used to sleeping at higher elevations(and with the constant traffic). what advantage does that have over a good sleep in a nice bed. you can wake up fresh at 1am and have a good hike. I would recommend a high carb dinner(spaghetti) and lots of water for dinner the night before.
Sleeping problems at Whitney Portal can be mitigated with the use of ear plugs and an eye mask. I do not even notice the traffic any longer in the hiker in campground and I rarely utilize a tent there.
For a newbie to Mt. Whitney, I do not care where they choose to spend the night there is going to be a lot of anxiety that will getting any sleep difficult at best.
I think the Portal experience is worth a bit of noise and traffic.