You can go back to the same floor, which is always the first floor when you enter the Lich Cave, what version are you playing on?
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.