You would be hard pressed to get to LAX by noon from Lone Pine even driving yourself, without leaving super early. And you would need to add an hour or more in case of traffic congestion. I think Reno is the preferred choice since it has that direct bus service and no traffic jams.
With public transportation heading south, there are so many different places for people to go, that you get dropped at a hub, and then have to take a new mode to the next.
If cost weren't a factor, renting and driving yourself would be the easiest.
