I have had over 60 LDs of varying awareness. There are definitely levels to it. I have had several LDs that were not very vivid and I did not even complete my intention for that night because I wasn't "all there". I have had others where I felt totally in charge. I even had the ability to remember my real life (which, in my experience, low lucidity does not offer).

It is even possible to increase awareness in the dream. I once spent the beginning of my lucid dream testing each one of my senses. This not only helped me experience things more vividly, but also solidified my awareness where I actually felt like I was there, instead of feeling like it was just another dream with the exception of being aware of it.