As scarce as is the Lite House
(now known as "Little Joe") is, especially one in "Project" condition, you might want to broaden your search scope.
May I sugggest considering a early 70's Hunter Compact-II for the following reasons:
(and no, I don't have one for sale!)
All molded fiberglass, 2 piece shell.
Better availability, In the past year I have seen 20+ Hunters for sale
and exactly 1 Lite House
, and it was turnkey ready.
Much lower purchase cost, esp in Project condition
Leaf spring suspension is easier to modify for off road use
Lighter, empty Lite house
is about 1050 lbs, Hunter is about 850 lbs
Lower overall height with top down, less apt to hit lowhanging limbs & animals, etc.
Only about 10" wider and 6" longer.
Some have a huge queen size bed, others have a full size bed and a bathroom.
Very easy to modify and update.
A similar rig is the Campster
Let us know if you need some pics