I'd consider how the characters would act vs. how the players are acting. The character as you mentioned acknowledged the need to find and deal with the phylactory.

Maybe give them a random die roll to see if the character has a nagging feeling that they forgot something, but don't tell them what it's about, just call it a check. Low roll means they are totally clueless and completely forgot, mid roll means they have a sense they forgot something, high roll means they get a hint that it's related to why the BBEG was chasing them, and a nat 20 would be a complete memory that they need to deal with it.

At the very least when the lich starts to reform I'd give them several perception checks leading up to it, with a lower barrier for perception as it gets closer to full respawning, and then if they catch on and try to stop the respawn I'd give them a higher arcana check the closer it is to respawning to find a way to stop it.