Ok, initially I copied and pasted a friggin' wall of rambling text, but I think it's better if I just give you my conclusion: The paradoxical state, or dreaming, is simply the conscious mind pulling together hundreds of stimuli and memes from a magnitude of waking states you've experienced in your life, while attempting to file away the most recent stimuli in a manner of not just compiling for later retrieval... but for a reference point to analyze the "new" data. It's when your teacher uses a metaphor or a mnemonic device to teach you something complex and novel, but your brain is doing it at such a rate of speed, it forms a narrative (albeit, barely coherent). It's the only time when the mind's temporal analysis is no longer linear because it's analyzing newer and old data as the same. When people are "lucid" they aren't bringing waking consciousness back into the dreams with them, they are simply engaging in the only true form of metacognition, that being, the mind watching the mind reading itself.
One sentence summary: The idea of being awake in your dreams is an instance in which the mind truly recognizes itself as process, rather than a state.
Why would lucid dreaming prevent "bringing waking consciousness back into the dreams"? I'm not sure what you mean by that.
Also, what makes you think that non-linear processing only happens during sleep?