You're the one who's in the unfavorable position to prove things, not me. You're the one who claims your game is provably fair. Argue that claim. I can't prove you're generating non-random numbers, and neither do I believe you do; that doesn't mean it's technically impossible for you or another party (whoever owns the node) to rip the users off. That's why I argue against, and say that you're faithfully fair.

You've yet to comprehend my point. I don't say that Lightning software is written in a way that makes pre-image generation non-random. I'm saying that it's entirely possible to alter the source code individually and make it generate non-random pre-images, since it's you who's running it.

But, can you prove that you don't own it? And if you do (which you don't), can you also prove that the person who owns it isn't ill-intentioned? No. Faith is required.