The dream I had last night seemed to be broken into fragments. Like I was in all these different places but there was no transition from place to place. I was in my school’s auditorium, then I was in a movie theater. But when I was in the movie theater, I think that I was lucid. I don’t remember the thought of “I’m dreaming” go through my head, but I remember trying to fly anyways but I fell. So I tried spinning to prolong lucidity or maybe I just spun for no reason but I remember saying to myself “When I stop spinning, I will be at my sister’s wedding.” That didn’t work either. So after this happened at the movie theater, I remember being in the poor, provincial town from Beauty and the Beast but everything that happened after that I wasn’t lucid. Was I just partly lucid or was I never lucid at all?
I have had dreams during which I lost lucidity eventually, so I´d say yes, partly lucid dreams are very well possible. What would speak for it would be your spinning, but I wouldn´t see the attempt to fly as a sign for lucidity, although it seems more likely to me that it was. For my, flying is often an indicator, so… might have been an LD. Congrats, Cheshire Cat. 
Hi Cheshire Cat!
Great nickname! 
Yes it’s generally what happens. You gain lucidity, it’s not necessary very high, then you can lose it, regain it, etc. As lucidity tends to weaken, a good tip is staring at your hands from time to time in a LD, it boots lucidity thus your LD can last longer.
Oh, okay. That fragment of my dream today seemed very different from the rest and it was probably because I was aware that I was dreaming.
You can be partly lucid in various ways. You can know that you’re dreaming but have little or no control, or you can act like you know you’re dreaming but not really do anything about it, or you can be lucid at different intervals.
I think going from partly lucid to fully lucid is my biggest challenge in LDing. I do get small impulses that I’m dreaming, but I just never “jump the hurdle.”
Also, if you’re an experienced LDer (or maybe it’s even possibly for inexperienced ones; I’m not entirely sure), you can also realize that you have complete control over your environment without actually grasping that you are in a dream. I’ve had this happen a couple of times.
Grr…I lost lucidity today also. I looked at my hands and saw that I had a 6th finger on my right hand, figured out that I was dreaming, but forgot.