The best thing you can do is to go to the NWS and enter Lone Pine, CA then move the little block in the map to about 10,000'. This will give the temperature and forecast for LPL. Or click here:
10 Miles W of Lone Pine, CAAs someone who has hiked this trail a lot in November, the chance of reaching the lake are good but there is a chance you will run into a bunch of snow. The good news is it will compacted snow since this trail is used a lot all year, unless it just snowed.
It would be best to have a some sort of traction device with you just in case. You will need something to cross the log crossing, if there is ice...I've only crossed these things with snowshoes when there has been snow about or just boots when there was nada.
