Just looked at the lake on Google earth. Both areas designated as "camps" on the map aren't campsites in the State Park sense with fire rings and picnic tables, so I'm guessing there's no need for reservations.
Hanging opportunities at the first campsite look excellent with a big stand of trees on a hill overlooking the lake. I'd be willing to bet that any ground dwellers will be wanting to camp closer to lakeside, so we'd likely have it to ourselves. The question would be what kind of trees they are, mesquite or post oak?
Walnut Springs looks like a more open area with little elevation, but there are trees back away from the water to the north.