Someone asked me: If you are truly conscious in a lucid dream, why is the likelihood of you remembering one the same as the likelihood of you remembering a regular dream?

Now I don't know, maybe you are more likely to remember LDs than regular dreams, but it got me wondering why you can ever have LDs that you don't remember if you're truly conscious? And are we truly conscious in dreams? What does it mean to be conscious?

Any thoughts?