There is not, and this time of year, it’s gonna still be quite snowy, i’d assume. Just under two weeks ago I went up Anderson via the Forsee Creek trail and the snow became and issue at around 8,500 ft. by 9,500 feet, i had snowshoes on and had left the trail to just go straight up to the summit along a ridge. It’s been a hot couple of weeks, but there’s still snow on the divide.
Judging from what i saw from above Dobbs Cabin today (Yucaipa ridge north face nearly snow-free below 8,500 feet except in the canyons) the snow has probably retreated another 5 or 600 feet on the north side of Lake Peak, which will be much like Anderson, snow-wise.
If I had to guess, you’ll be snow-shoeing from dry lake up past lodgepole springs to the pass, and on to lake peak, with similarly steep terrain the whole way.
Normally, in the summer, i’d go up Lake Peak from Mine Shaft Saddle, which would also be a good way to do it from Fish Creek Saddle, though the elevation profile looks about the same if you just go straight to the summit of Lake Peak from Fish Creek Saddle.
AFIK, there’s no trail to the summit of Lake.
Hope that helps!