I think that honestly the best workable concept for a lucid dreaming game would be as such:

Randomly generated world and scenarios, just like in LSD Dream Emulator or Minecraft. This is the easy part.

The hard part is coming up with a gameplay mechanic that mimics lucid dreaming. I honestly thought that an interesting way of carrying it out would be to have the character move autonomously (not under player control) and carry out scenarios. (Such as panicking and being late for school, or other common dreams). This would be the non lucid mode.
In order to become lucid, the player would 'click' on anomalies in the world. Perhaps the text changes when you look away from it or there is an object that is out of place. As you found more and more dream signs, a meter would fill up, and when it hit the top, your character would reality check, and you would become lucid.

From here you would gain full control of your character. You could now walk in any direction you wanted to and explore any region.

As you 'level up' from getting lucid more often, you begin to unlock new abilities.

One of them might be a 'WILD' button that appears before you begin a dream, and gives you the option of having an alternate way of becoming lucid. I'm not certain the exact mechanics of this, but it should definitely happen.

Dreams may start to become clearer and longer. You may have to click on fewer dream signs to become lucid and may not wake up as quickly.

Also, as you level up, you may unlock dream control techniques such as dream stabilization, flying, and spells for fighting nightmares.