First, I check the overall condition. In my experience, even a cosmetically nasty lever action can still shoot just fine--and I've never seen a good-looking one that wouldn't shoot. For example, a little surface rust is very common, will not affect function, can be easily removed, and knocks the price down. Dings in the stock are usually a sign of "experience," and don't bother me. (Cracks or chips bother me, though.)
Rifles were made to be shot, so I check the action to see how worn-in it is. (A lever action has to be pretty beat up to be worn out.)
I prefer Marlin to Winchester rifles; Winchesters rattle a lot even when new, so some looseness in the action isn't a bad sign. On Marlins, though, I think twice if it seems loose.
I generally look at the bore, to make sure it's not pitted or too dirty. (I've never seen clean bore on a used rifle, especially in pawn shops.)
Holding the hammer, I squeeze the trigger to make sure it will release properly. I also check the half-cock safety.
Overall, it's been my experience that there are few problems with lever-action rifles that can't be solved by a good cleaning.