I think I just had my first lucid dream last night, but I’m not sure. The first part of it I’m sure was not lucid. A bunch of random strange things happened that eventually led me to a mall. Once I got into the mall, I distinctly remember being very excited and even thinking “a lucid dream!” I felt like I had control, because I was jumping around very high (almost flying) and I was able to change people’s clothes by snapping my hands. I did those things for a while, and then I remember not being very lucid at all for the rest of my dream. So the question is, can you be lucid in one part of a dream, and not lucid in another part of it?
Yes, lucidity is very sensitive and manipulatible. You can swap endlessly from lucid to non-lucid. But after all, since you got lucid in that dream, I would still call it a lucid dream. 
ya I always experience it sometimes when I’m having lucid dreams. One minute I can be able to do things like make a fireball then its like im slipping away or I’m having self doubt and then the fireball completely disappear.
That indeed is one of the greater obsticles for most people who try to learn to dream lucid. But it is certainly trainable to keep your lucidity longer, even up to dreams that would seem to last weeks for the person experiencing it.
I wish I was as good as LaBerge 