I had an LGR that I sent to Champion's Choice for a rebuild. As I recall, I sent them just the action out of the stock. I don't recall how much it cost, but they did a great job in a very reasonable time frame. I'd suggest giving them a call for pricing. Nice folks, who understand great classic 10M guns.
here a part diagram, it looks like a very busy rifle internally and if air is coming out of the barrel the valve is leaking but at this point the rifle needs a replacement of all wear parts for it future
http://www.carlwalther.com/views/ev_lgr.htm
you could clean the valve and get it working but I have never been in one of these
If it is bleeding air out through the barrel, it is almost certainly an exhaust valve seal that is leaking. You should be able to get the seals from JG Airguns.
LGR disassembly and reassembly are very straight forward (screws and "c" or "e" clips) until you get to the valve retaining ring. To remove the retaining ring you need a two-prong spanner. I ground my spanner out of an extra-deep 10mm socket wrench. Once you have all the correct tools, it only takes 10 minutes to replace a leaking exhaust seal. If you take this on yourself, please note that there is a small screw that engages a slot in the valve body to keep it from rotating. This little screw will have to be removed before you can remove the valve from the receiver.
The exhaust seals wear a lot faster than the piston head seal. I would not try to replace the piston seal unless it was absolutely necessary. Its a much bigger job.
The most time consuming step in replacing the exhaust seal is making the spanner for the retaining ring. If you don't want to go to the trouble, I would suggest sending it to Pilkington Competition. Although I would avoid replacing the piston seal if doing the job myself, if I sent it out for re-sealing I might ask for a complete rebuild, including the piston seal.