You can still forget long term--it just means short term memory is intact. If you wake up directly from a lucid dream, and realize you are late for class, I doubt the dream will enter long-term memory. If you have a lucid dream in early night, and continue sleeping after it, your mind will wipe that dream from your memory before the next begins.

But yeah. As far as remembering dreams as you wake up, lucidity helps. I wonder, if by lucid dreaming often, you could turn on the short term memory receptors during normal dreams as well?