I'm having this same problem actually on version 5.1. When you enter the Lich cave, it automatically starts you on the highest floor you last visited instead of Floor I, so I can't go back to try the Lich Pool event.
EDIT: You can reset the dungeon with one of the ladder escape items you get from entering it, it will always reset at 1 so you don't have to redo anything to get the Lich event to work.