Lucid dream?

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?

If at any point during your dream, you realized that you were dreaming, then yes, it counts as a lucid dream. Lucid dreams are usually harder to forget than normal dreams, but it is certainly possible to forget them completely. Also, it is quite common to lose lucidity part way through the dream, but as long as you realized you were dreaming, then it was indeed a lucid dream. Good Luck in your future efforts and I hope this helped clear things up a bit :).