When I did it I had the whole second floor of the lodge to myself. The caretaker also gave me his approval. The LT shelters are a little different than the AT ones. Most of them are more like a small cabin or lodge then the standard 3 sided AT ones.
I think that as long as you are not damaging the shelter or inconviencing anyone else, there isn't anything wrong with it. If there are other people around I would hesitate to hang there.
Is that too much to ask? Girls with frikkin' lasers on their heads?
The hanger formly known as "hammock engineer".