Hi RocksOff,
Picking up on the day of entry pretty much means you are doing an overnight hike right? Overnight permits can be picked up on the day of entry up to 10 AM. If you don't show up by then, they give it away. ...EXCEPT if you call in and ask them to hold it because you are coming in later to pick it up. I believe this information would be included in the printed material sent to you when you get a reservation. However, this being the first year permits are available online, you might be emailed the information.
As for hiking in a short distance and camping, that requires an overnight permit, and the Whitney Zone rules and quotas apply, even if you stop and camp at Lone Pine Lake. So that would be the same as any Mt Whitney overnight permit.
You don't need to pick up the overnight permit the day before. That is the rule only for Day Hike permits. However, if you ARE there a day early, and if the quota for THAT day is not full (due to no-shows and cancellations), then they can change your permit so you could start that afternoon or evening if you want.
(I am not sure the following....) Getting there and picking up your permit at that 10 AM time the day before might be ideal for moving up your start date by one day, since there are always no-shows, and the walk-in people without permits aren't able to even ask for the no-shows until 11 AM. Like I said, though, they might not let you do this, and instead tell you to get into the 11 AM drawing and compete with the other walk-in people.