This definitely sounds like a lucid dream. No one can tell you for sure, only you can determine whether it was a lucid dream.
Don't doubt yourself too much though, I know it can tempting to chalk up a real lucid dream as a false lucid because you are not very experienced and don't know how lucid dreams should "feel", but don't. It only discourages you.
Btw, if it was a false lucid, you'll know soon enough. Once you have a high level lucid dream you will easily be able to tell the difference between a false lucid and a lucid dream.

p.s. It is VERY common for lucid dreamers to become lucid for no reason. I've had dozens of lucid dreams in which I just suddenly noticed I was lucid but didn't remember how, why, or even when. Some lucid dreams feel like I had always been lucid, yet I know I wasn't. It's a very strange experience for sure.