You were aware that you were dreaming. Ipso facto, you had a lucid dream.

It sounds like you need to work on stabilizing the dream, also make sure to RC after becoming aware. It will sometimes give you a more "fuller" realization that you are indeed dreaming. Work on doing clarity increasing techniques as well, such as dream spinning and had rubbing. These are things you should have done when your dream was falling apart.

By the way, there are different degrees to lucidity, that's why I mentioned the reality check. You want to be as conscious as possible in order to be able to stay within the dream, and lucid... and don't forget to remain calm!

Welcome to the forum