Echoing what has been said already. The service history on an LT is of paramount interest as there is a list of things that are of concern and if already repaired properly, should all be in the PLUS column. If not, they are in the MINUS column as they will need to be addressed most likely sooner rather than later but every bike is different due to riding style and environment. The mileage is of little concern unless the oil has never been changed
Any oil around the mating surfaces of the transmission and bellhousing and engine is a minus.
Major items of concern would be brake lines, final drive from failed crown bearing, clutch due to seal failure and contamination and fuel lines inside the gas tank and the male portion of the fuel quick disconnects if still plastic and not metal.
Look for upgrades like shocks, windscreen, seats and lighting, rear floor boards. Check the top case latch as they are pot metal and they do fail. No one is currently making a replacement so it would be a new top case from the dealer or ebay and then you are subject to it failing again as there have been no improvements. Check the top left and right corners for signs of metal fatigue. Pressing down on the top as you open and close to relieve some strain on the latch is a good idea.
They are fantastic bikes to ride and once you get past the major items should they fail, are fairly reliable although as Voyager mentioned, a complex bike. If you are decent at wrenching, you can keep costs down but all know, a trip to the dealer on an LT can easily go into the quad digits for some of those repairs. I have owned mine for 5 years and although none of those had failed, I have bigger plans eventually so I have just gone through all the items and done those repairs making the recommended upgrades to parts along the way. I had the time and money and like the bike enough to have just done it on principal. I can't say it wouldn't die along the way as stuff happens but I would get on mine and go anywhere and not think twice about one of those systems failing along the way at this point. That is a good feeling so service history and receipts if the owner did the repairs is important.
If you are close to someone who is already an LT owner who could go look it over with you, that would be a benefit. Maybe someone around Jax will pipe up and offer.