Inyo NF has posted their last lottery update before the March 15 cutoff here: Mt Whitney Lottery Progress Report

8,744 applications submitted as of March 10

There is a nice chart on their page showing the first choice numbers from all the applications. Viewing that, I can see:

For Overnight permits (Quota 60 per day):
First overbooked date: Saturday May 10, and every Saturday after that.
Most requested date: Friday, Aug 1: 763 requests. (Less than 1 in 12 chance)
All requests will be satisfied after Sunday, Sept 21 (except the 154 requests on Thurs Oct 2 ...weird).

For Day Use permits (Quota 100 per day):
First overbooked date: Saturday June 7.
Most overbooked date: Saturday July 19: 541 requests.
All requests after Saturday, Sept 13 will be satisfied.