Originally Posted by Steve C
You need to try your luck on recreation.gov/Mt Whitney

Unfortunately they aren't updating that site with the no-shows, etc, this year due to the complications with COVID-19. I think some permits do show up on that site occasionally, but it is rare and random.
I saw open day hike permits for tomorrow (July 17) earlier this week. They were all taken in about 10-15 minutes. However, I haven't seen any weekend permits even for solo day hikers despite checking that site pretty regularly over the past few weeks. Those are incredibly rare.