[RPG] Would a lich remember someone they knew in life

All the information about flameskulls in 5e is on page 134 of the Monster Manual.

It is stated that a flameskull "only dimly recalls its former life," but this refers to the life it had before it became a flameskull at all. There is nothing to suggest that flameskulls have a poor memory in general.

In the description of the flameskull's rejuvenation, it says, "If it can no longer fulfill its intended purpose, the re-formed flameskull is beholden to no one and becomes autonomous." This suggests that the flameskull can remember things (such as its orders) from before its rejuvenation.

A flameskull has an intelligence of 16, suggesting it should be able to plan and reason strategically. Casting fireball the moment it rejuvenates seems like a reasonable strategy if the last thing it can remember is being smashed the moment it rejuvenated.

In the Curse of Strahd module, it doesn't give an exact year that these events take place. Everything can be kind of fluid because of the nature of Barovia, which I won't get into because that might be a bit spoiler-y. However, according to the module:

Strahd had all the female dusk elves put to death around four centuries ago as a punishment for Patrina's murder.

In terms of Barov's handling of the dusk elven royalty, again, no hard number of years, but in some information about Rahadin in an Appendix, it states:

Rahadin, the dusk elf chamberlain of Castle Ravenloft, has served Strahd's family faithfully for nearly five hundred years.

So it's safe to assume a range of four to five hundred years ago for those events.

As an aside, fantastic character development potential. I would be super excited to play with/DM for your PC.