My family has had a cabin on forest service land since the mid 70's. I'm not sure if it's the same sort of deal but we own the cabin and hold the lease for the land that the cabin is on, if the one you're looking at is the same way then the initial cost is probably to buy the cabin. These cabins are starting to get expensive, when we bought our cabin it was about as much as a nice car and now similar cabins in the area have been selling for the price of a decent house. From what I understand there are two ways that the lease can be an issue, the first is that the forest service can decide to change the cost of the lease dramatically the second is that you can lose the lease if you let the cabin get too rundown.
I remember a few years ago we were concerned because they were re-evaluating the lease rates nationwide and in some areas raised the rate by as much as 2,000%. Luckily they only raised our rate a small amount but at the time we had family discussions about whether we would rent the cabin out some or just sell it if the cost went up too much.
I have never heard of anyone losing a lease due to condition of their cabin but once every several years they go through an area to check if cabins are in compliance with the rules. Then they send out letters to the cabin owners with a list of any necessary repairs and a date that the repairs need to be done by(several months later). Last time they checked our area we were told to repaint the exterior which we already were planning on and that we needed to replace a window that had a small crack in it. They didn't seem to care about some of the other obvious issues we were planning on fixing that summer though.
In my opinion the biggest issue with these forest service leases is that they heavily restrict what sort of changes you can make to a cabin and there are silly little rules like what color of tarp you can use to cover your woodpile.