iserith
Magic Wordsmith
Recalling lore is explicitly an ability check in 5e.
No. Recalling lore is a task. A task may or may not call for an ability check.
A player simply deciding that he know she is a Lich(success at the intelligence check) is the same as a player simply deciding that his PC jumps 5 feet farther than his strength score(success at the strength check).
No. The player says the character thinks the NPC is a lich. The player has not established that the character is trying to recall lore. There is nothing here for the DM to adjudicate.