Dart will remember important plot points and a vague sense of old!Lucy but I didn't play with her so nothing very specific. She definitely won't remember the Terrible Things that Lucei did.
Narumi will remember more than Dart! Especially about being related to the blonde Pavo kid. But he'll remember it as if it was a dream and the details will fade since he doesn't care that much. He will remember the name Narcissus and he might actually start using it because he likes it!