Yes, you recall correctly. taking each point by point: th trailhead near the Wp store is in the national forest, but not in wilderness. Then you reach the North Fork route forking to the right. That is also not yet in wilderness. Just across the stream, you enter Wilderness at the JM Wilderness sign. You are not yet in the Whitney Zone. ANother mile or so and the Lone Pine Lake trail forks to the left. ANd finally a little beyond that, is the sign where you enter the Whitney Zone, and need a permit even for a day hike. No permit for a day hike to Lone pine Lake. to stay overnight at Lone Pine Lake, which is permitted, you need a wilderness permit, but not Witney Zone permit. At least theoretically. I don't know whether INyo will actually issue this permit.
