Though you were real close, it sounds like you never quite came to the conclusion that you were dreaming. You must be completely sure you're dreaming for it to be a lucid dream. In the process of concluding something, you might think "Is it? It might be. It must be. It is." It sounds like you didn't get to the "It is." part of the conclusion process. So, I would say it's non-lucid.

Try listening to those binaural beats again!