> the lottery for day climbs was moved to 2:00 pm, like it used to be (?)

That is my understanding. I am waiting to hear back from Inyo regarding the July numbers, and I hope to get this all confirmed then. I am not sure there is a lottery at 2 PM, but I am more sure that the unused permits become available about then.

> can you tell me the approx size of the food lockers at the trail head?

They're actually closer to the parking spots than the trail head. And they're big. Big enough for several medium sized ice chests. But they are used by lots of people, so try to keep your stuff to a minimum -- grocery bag or some similar container. If you can remember, put a note on the container with your name and expected return date, so it can be removed if you forget to take it out.