Your second dream sounds a bit like a pre-lucid where have the idea that you might be dreaming but for some reason ingore it or come to a conclusion that you're not.

Anyway, those definitely aren't lucids because you didn't realize that you was dreaming. Remember: A dream is a lucid dream if, and only if, while dreaming, you're aware of the fact that you're dreaming. It doesn't matter whether you have control over your dream or not.