The only loop trail i know of that is any good distance is the west end...richards, sandy branch, and north and south wilderness loops that all connect....should be able to get about 15 miles or so in...and you could extend that by going up the main trail and backtracking. You can get maps at
http://www.lshtclub.com/
Need any company? Im looking for partners or a group to do some of the LS trail.