Lucidity is a scale to me, a continuum between being completely conscious of being in a dream and being able to do exactly what you want on one end and just having absolutely no idea you're in a dream on the other. Most of the the time you're bound to fall somewhere between those two extremes.

I think the cut-off point is simply just having that "aha" moment and what follows can either be complete control and understanding one is in the dream state or just going on a little adventure and seeing what happens, still keeping the idea of being in a dream in mind. Where lucidity in it's proper sense disappears after the "aha" moment is still something that can be debated.