I've created a "Lights Out" puzzle solver/trainer for Android phones. This includes all 4 configurations (Circle, 3x3, 4x4 and 5x5). I use it myself for solving 5x5s.
You can download it here:
I've looked at the Monastery puzzle, but that requires finite matrix mathematics, which will take a while for me to master. Also contemplating a Reaver puzzle solver/trainer.