I think that to be lucid has two requirements: You should know that you are dreaming, and you should be consciously making decisions. To me, the latter one is actually the more important.

I have had forgettable dreams where I knew that I was dreaming, but had no consciusness. To be conscious is quite different than attaining memories. It is hard to explain this, and I did not understand this at all until I learned meditation.

On the other hand, my conscious dreams are about as remarkable as my lucid dreams (although I expect that this will change as my skills improve!). For example, once I saw manta rays flying around in the sky and I was in the same state of consciousness as lucid dreaming, except I thought that I was hallucinating! I had a real thought process, rather than just having ideas popping into my head for no apparent reason, and I was even testing my vision by looking out of the corners of my eyes. I noticed that if I would clear my head the manta rays would slip out of vision and this proved to me that I was going insane. I became very worried!

However, most lucid dreams are some mix a different levels of understanding and control anyway, and if you know you are dreaming then you are probably making good progress!