FDR, I just checked the map of that area
, and I see that those lakes are in the 10-11k elevation range.
Comparing that to other areas, the main Mt Whitney trail is pretty much free of snow to Trail Camp, 12,000', and the snow-depth gauge at Cottonwood Lakes
(at elevation 10,150) shows zero snow since mid-April.
I think you should enjoy a great hike... except maybe for the weather. Here's the NOAA link
for that area.