No, mental illness runs in my family so I consider it too risky. But I've been told by a friend that lucid dreams occasionally, that lucid dreams are different from LSD/mushrooms in that you have much more control over the experience and it seems more real.

There's definitely other psychedelics that produce "real" seeming illusions but I'm not aware of any that give you direct control over them like lucid dreaming can.

Simple. They don't. My stream of thought during a lucid dream isn't much different from my stream of thought during normal, sober waking hours - it is just the stuff going on around me is weird and I have different constraints on what is possible.

On psychedelics, I view the world and myself differently. I know I'm on drugs. My stream of thought is different I'm obviously still in my house, for example, and I know I can't fly or make things appear out of thin air. By the time any hallucinations would be dream-like (strong and heavy), I freaking know I'm hallucinating. Even with lighter things (much more common), I know it is a hallucination. I know that my painting doesn't really move like that, for example.

They're completely different. Psychedelics change your perception and thought processes in a way that's completely different than a lucid dream.