I've created a Lights Out puzzle solver/trainer using the DDO layouts (circle, 3x3, 4x4, 5x5) for Android phones. I use this myself for the 5x5s - I solve down, and then enter the final row in the solver on the phone, and then use it to solve the puzzle. I find this a lot easier to use than switching back and forth with another app or a web browser.

Looking at the Monastery puzzle, there's some finite matrix mathematics involved in that solution, and I'm not sure I can master that anytime soon.