My group stayed at Lone Pine Lake on our Whitney summit trip. It was a great place to spend the first night and following morning.
A huge advantage is being able to acclimate to the elevation. Lone Pine Lake is approximately 10,000 feet, and spending a night there helps to be ready for the summit elevations.
It is a pretty little lake, surrounded by sheer granite cliffs on one side, views of the valley below on another, and high mountain pine forests on the others. My group of 5 found plenty of places to camp. The lake does have some small fish, but fishing was much better further up the trail at Mirror Lake.
We secured permits for the summit, and this was one of our planned stops. The Whitney Zone is about 1/4 mile further up the trail. You are required to carry WAG bags here, as well as bear canisters. We filtered water from the lake. And as a side note, we found that on the far side of the lake, you can actually get limited cell service