I've had lucid dreams for around 17 years now or 2/3 of my life, the only real consequences is length of time dreaming, time dilation & conflict escalation. All other claims sound improbable to me & likely stem from preexisting circumstance.
For my experiences, the length of time spent lucid dreaming has steadily increased over time. It started insignificant enough, around fifteen minutes to half an hour every night. Now it's often between an hour or two every night, which can get annoying at times. This can also become exceptionally distorted if I wake up to my alarm & hit the old "snooze" button, going back to sleep. In these cases it isn't irregular to experience a (1:10 min ratio) time dilation. I can only validate time dilation during these periods of time, but suspect it occurs during normal sleep as well. I'm still rather young, so in the back of my mind I wonder how extreme this time dilation can get.
The other primary consequence I've experienced is conflict escalation. I strongly believe my lucid dreaming evolved as a consequence to nightmares. My ability to recognize when I'm dreaming, also gave me a quasi sense of immortality. Knowing you can't die when your enemy certainly can is an intoxicating feeling for anyone. Nightmares ceased existence soon after, but what soon came can only be described as an arms race. Instead of a nightmare dream-scape, my controlled dream-scape can sometimes encounter intruders. These intruders always meet a quick demise, but only because I've evolved faster then they apparently can. These interruptions although infrequent are extremely annoying & drag innocent entities into the conflict. I've never been a religious person, but through lucid dreaming I understand my Creator's paradox. To be all powerful & yet unable to save everyone. For those who think your lucid dreams are a theme park for all manner of immoral mischief, consider this. In the beginning I was reckless, but was confronted by an individual with a simple question. It asked me, "Just because you gave us life, do you think we don't exist?". I never answered because I didn't know how to. I could only think what If I was in that entities place facing my Creator. Even if at the time I was unsure, how crushing would it be if your Creator told you that you don't exist? For those who think lucid dreaming is an escape, they're vastly misinformed. Lucid dreaming is the opportunity to be a god, but what you do with that power defines you as a person.