I would read up on Mt. Langley, another 14er, with a great view of Whitney, and with a trailhead near Lone Pine. And if you ascend via New Army Pass you'll even get to hike switchbacks. I would suggest sleeping at Horseshoe Meadows (no reservation needed) and getting an early start, as you would for Whitney. There are even some decent YouTube videos of people hiking up Langley which are very useful prep materials.
I would also suggest that you read everything that you can about walk-in permits. The lottery is by no means the only way to get a permit, especially if you can free up some time mid-week.
Edited by Goose (02/13/19 11:55 PM)