I agree with NeAvO. I'll just add that you can also be lucid and have no dream control, so it works both ways. In fact, being aware that you are dreaming yet having no dream control is exactly what "low-level lucidity" is, at least, at the lowest level. That's not to be confused with the fact that you can be on a higher level of lucidity and have the faculty of control but choose not to exercise that ability. Sometimes it's nice to simply be a passive bystander and watch how the dream unfolds itself.