There is (are?) campsite(s) around there. Closest and probably most expensive is Fontana itself.
It's about a 2 mile drive from the Lodge, down at the bottom of the Dam on Hellbender on the way to the Dragon.

Fontana Village Resort. Campground

Tent sites are $20 to $30 a night. You might get something cheaper near Bryson City but that is about a 1/2 hour drive (or more, right everyone?)

But Rooms are only $79 a night - you might find someone willing to share a room.