I've never, ever been so stressed by a game of Lights Out. I even think I worked up a sweat. I never ever expected that. It's incredible how much the timer and story changed the feeling of these games.
Overall, I enjoyed it a lot, despite the constant crushing claustrophobia of impending death. :-)
I only have two criticisms. First, the mechanic wasn't always obvious. I was able to guess the other ones, but the peg jumping made me have to ask. Maybe a hint button would have been nice, but given the theme, it might be better without. The lack of understanding leading to increased frustration and despair. So maybe you should just disregard this one.
The second one seems to be echoed by others; give a restart button if people fail the initial puzzle. It's annoying to have to go by the menu. (I had to do so three times).
Apart from that, top marks. I'm stunned!