A very long shot but here it goes: Had a similar problem with my newly acquired JM, balls drained but machine failed to register them quite frequently. Checked the opto-boards and everything was fine. The problem was that the balls were magnetized as the game frequently shoots them into the magnet of the moving hand assembly. Somehow this was enough for the drained ball not to roll down the trough properly or other balls sticking together and thus prevent them from advancing and hence problems with the kickout.

LotR has a magnet as well, so you might eperience something similar. More obvious would still be the opto-board of couse...

Edit: Put a few other balls in the machine and test. You can also take out the balls from your LotR and place them on a level surface. If you touch them together, start moving one around and the other follows you have magnetized balls. The do not stick in all orientations, but you should be able to see whether this is your problem or not.