I was put off from answering here because the OP has an aggressive, almost angry tone, and makes some strange claims that I can't agree with.

When I become aware that I'm having a dream, I KNOW I'm lucid. I might even confirm it with a couple reality checks, but by that point I already know. Why is it necessary to prove it? To use the fire analogy presented above, if you build a fire and cook your dinner in it, is it necessary to prove to yourself that you actually built a fire? I think the real question here is semantic... what's the difference between knowing and proving? And this is probably unanswerable, because let's not forget, in the entire history of human thought, no-one hasbeen able to so much as prove that reality itself exists. We haven't made it past "I know, therefore I am". Unless I missed the memo on that one. So, while what we know as concrete reality does have a very different character to it than dreams, we still can't actually prove that they aren't essentially the same type of phenomenon. Basically because the only apparatus we have for doing experiments is our own subjective senses sending signals to the brain. We have no way to prove the validity of any external devices because we can't really prove that such devices themselves even exit. If we can't prove the difference between waking reality and an ordinary dream, how then can we prove a difference between two different kinds of dreams? I'm afraid it's an area where we can never have actual proof of the kind you seem to want - we can only rely on our own experiences.

However, to be truly lucid a dreamer must be aware that the place, plot, and characters that he is experiencing come from his own mind, and nowhere else, even when he's watching the dream as if it were a movie (an extremely low level of lucidity, IMHO). To assume that "it's all from somewhere else" either means that you are not entirely lucid, if at all, or else you are looking at the dream as something else, like an OBE or shared drea
There's a basic mistake here - in that while every element of a dream is produced by your mind, it comes from the subconscious. Not from consciousness. So while it's true that every element of the dream is created by your mind, including the dream environment itself, in many lucid dreams we fail to recognize the full implications that everything is a creation of our own mind. To realize this means you're having the highest level of lucidity, or at least an extremely high level of it. Personally I haven't even reached that level yet, though I have been absolutely aware that I was experiencing a dream and able to control some aspects of it. You've already admitted that you acknowledge 'levels of lucidity', so I don't understand why you automatically expect every lucid dream to come will full awareness that every character and every element in the dream is a mental fabrication? This statement seems to imply that anything less than absolute highest level lucidity is not lucidity at all.