By dream recall, do you mean recalling dreams and writing them down or just recalling dreams upon waking up?

Writing down dreams isn't needed to have lucid dreams, but being able to recall dreams upon waking up is. It's true that lucid dreams tend to be a lot easier to recall upon waking up, but not being able to recall dreams at all upon waking up shows a lack of awareness during those dreams that is needed to become lucid.

Recalling dreams allows you to learn from those dreams, which can help you become lucid. I think what is learned from the recall is more correlated with lucidity than the act of recalling itself. Writing down the dream helps in being able to recall it for a longer period of time.