I don't think of the lucid dream world as inner or in my mind. Although it may be, it doesn't feel like it. Scenes, characters, and transitions are normally not my own making. It is a complete alternate reality to me with fluid rules that govern it, as opposed to the concrete rules of reality. I recall one dream where I was semi lucid and something I was about to do I knew would wake me up. I was really enjoying my lucid world and felt sad that I would eventually transition to that "other place" as if they were both valid realities in their own right. Both realities have their pros and cons.