Last night I became lucid and did something I wanted to do but wasn't what I had specifically planned for my next lucid dream. Later I had a false awakening into a non-lucid dream and didn't even remember right away when I woke up that I had had a lucid dream.

I suspect this and other dreams I have had to be fake lucid dreams, or lucid dream in a dream. Or maybe it's just a low level of lucidity, and I wasn't completely aware. What is this? Does it count as a lucid dream?