FWIW, the permit process for Whitney changed last year, for the main Mt Whitney trail. There are no longer any walk-up permits issued during the quota season. Everything is by reservation only. I believe you can still get a walk-up permit for the North Fork Lone Pine Creek trail if you're looking at the Mountaineers Route.
https://www.fs.usda.gov/detail/inyo/pas ... 869#walkin
"No walk up permits are issued at the visitor center for Day Use - Mt Whitney, or Overnight - Mt Whitney Trail. These permits are by reservation only for trips beginning May 1 through November 1.
Reserve space from last minute cancellations or group size reductions on Recreation.gov. Reserved permits can utilize Will Call and Night Box Service if called in the day before the trip. Phone line closes at 4:30 pm.
Walk up permits will continue to be issued for other Inyo National Forest trail including overnight North Fork of Lone Pine Creek, or trips that exit at Whitney Portal."
Here's a link that shows CA snowpack relative to past years. The High Sierra are more or less in the "Central" area.
http://cdec.water.ca.gov/snowapp/swcchart.action