tdtz is correct on the permits. On Meysan Lake, dayhike permits are not required, but overnight is.
No matter where you go in Inyo National Forest, whether inside Whitney Zone or not, you ALWAYS need a permit to camp overnight.
You only need a day hike permit if you hike within the Whitney Zone (and of course Half Dome in Yosemite). All other trails and areas may be day hiked without a permit.