My LII father can, I've no idea where he heard the concept from though. He explained it to my SEI sister (I'll call her Cookie from now on since she likes Cookie Dough Bites) and I when we were very little, and presented it as a coping mechanism against nightmares we were having. I lost much of the "ability" in my teen years, but Cookie can still lucid dream and would do so nearly nightly before she got sick and began medical treatments.
Sounds silly but evidently there are "
levels" of lucid dreaming, and it is a spectrum on each level.
Cookie is most likely a Level 4 lucid dreamer, which is the "highest level", since she says she can do anything in her dreams. She's immediately aware that she's dreaming, she knows what's in "the dream land" and what's IRL, and she immediately has control of her actions in her dreams. She flies in her dreams, terraforms the environment, changes the weather, liquefies people if she wants, changes the actions and thoughts of others
without persuading or communicating to them... things like that. Her imagination seems to be the limit on what she can do. She's super casual about it too without being hoity toity, if I ask her about it she'll say something along the lines of "You can't do that? Dad taught it to us when we were kids." haha.
I was never on that level of mastery. I could fully control my actions, interact with everything in the environment, and was beginning to terraform and shit (pretty gardens ftw), but I don't ever recall changing the thoughts or actions of others. Maybe a few times by accident. Current day, when I do dream, I do still have the awareness that I'm dreaming and I still react to my dream environments with limited control. But I have a lot of trouble doing so and don't have the mastery that Cookie does, where it was like a RPG where I could do fuckall.
As for my dreams feeling real, the first step of lucid dreaming is becoming aware that you are in a dream, so I can't say anything feels truly real. I would have fun in my dreams most of the time, and I still have fun dreaming, but I still knew they were dreams you know? And a big part of dreams for me is disassociating myself from them after I wake up anyways, no matter how much I enjoy whatever they can offer me (fun, symbolism, introspection, etc).