Hi! Welcome to the forum.
A lucid dream is a dream, in which you know you are dreaming. So it sounds like you had quite a few. If you knew that you were dreaming in the second part (the nightmare part that is), then you had a lucid dream there too.
If you are interested in all this and want to keep doing it, I suggest you start a dream journal. It will help you improve your dream recall, or help you spot dream signs.

See ya around!