che, congratulations winning hiking slots in the lottery!

If the first family can score a camp site in the Whitney Portal campground, they could spend the first night there. If they can't get a camp site, there are one-night walk-in camp sites that are usually never full. There is a map/discussion in this thread, best map on second page: Sleeping in your car at Whitney Portal

Anyone can DAY hike up to Lone Pine Lake and back without any sort of a permit. And doing that doesn't affect what you do on your overnight permit. Now camping at Lone Pine Lake is another matter--You are required to have a wilderness permit to camp there, and the same permit that you won in the lottery is what you need.

Only thing about permits to camp overnight: You may not enter a day earlier or a day later than is stated on the permit. You can exit earlier, or spend extra nights, but the entry date is the one most important thing that cannot change.

Depending on your starting date, there MAY be unused walk-in permits available for the first family. They should ask when they arrive to pick up the permit won in the lottery. There are many no-shows, and they just might be able to score enough of those slots to go ahead and start a day early. If that works, they would effectively drop half the slots on your permit, but could go ahead and pick it up for you, and then request the walk-in permit so they could hike up to and camp at Lone Pine Lake.

You didn't say when your start date is, but the Unused Permits pages give you an idea of how difficult it would be to get walk-in permits a day early. Unused Whitney Permits 2017