The Drunk Monks' First Aid room is in the base floor, far left. There's those three "switches". They must be connected to the door.
This is the low-spoiler guide for "Entering the Drunk Monks' First Aid room" puzzle in Lancelot's Hangover. Unlike in normal walkthrough, you get gradual hints on how to solve the puzzle. Click the big button below to see your first hint. If the hint contains a spoiler, you will be warned about it before clicking.