Lucidity simply means you're in a dream and know that you're dreaming. That is precisely what the definition of the word means.

"levels of lucidity" are very subjective qualities of a lucid dream, and depend on the person expressing it. For me, fully lucid means that I have relatively decent access to my waking memory, know 100% that everything is in a dream and remind myself of this to have precise dream control, am able to remember to stabilize a dream and recall dream goals, and have no fear whatsoever of my dream environment. But, this depends. You can still be completely lucid and aware that you're in a dream, and something you're attempting can not work. You may realize 100% that you're in a dream, but can't access that memory from waking life. Maybe you're aware but forget things, just as you can be aware but forget things in real life. Maybe you're lucid, but you realize that no matter what you can still feel pain, so you're afraid.

Really, being "completely lucid" doesn't mean anything. Make up your own definition, set your own standards, because as far as I see it, it is completely impossible to come up with an objective scale for lucidity since we have no way of comparing our dreams to each other in an appropriate manner to make such a scale.