Good question. I have to confess that I have many times not distinguished memories of dreams from real memories, thus making myself look like a fool in diverse situations.
But none of those dreams were lucid, they were simply vivid and totally believable (no funny things going on), that I put them on the archive of real memories.
On a lucid dream you're lucid because you realised you were dreaming in the first place, therefore all that happens from then on, will be stored in your dream memories. Also it's not likely that you have a lucid dream and not use it to do extraordinary things like flying and going to the moon, so even if the memory is very vivid, you will know it is from a dream, and there's no chance you will come to your friend saying "oh, remember that day when we were in Jupiter?" convinced it really happened.
The chances for this to happen with normal vivid dreams is far far greater, than with lucids in which you KNOW you're dreaming, therefore no place for confusion.