Lunatic Inquisition is basically Southsun Survival on the GW2 Mad King's Labyrinth map.

Each game starts with one player as Courtier (enemy). All the other players are Villagers. Villagers try to avoid being killed by the Courtier(s).

When a Courtier kills a Villager, the Village respawns as a Courtier. Tension grows as the game progresses, with more and more Courtiers, and fewer Villagers.

How do you get to Lunatic Inquisition?

To start a game of Lunatic Inquisition, enter the Mad King's Labyrinth through any Haunted Door with a pumpkin icon. Once there, talk to the Lunatic Boatmaster NPC (he's a big charr standing next to the waypoint). Tell him you want to enter the Lunatic Inquisition.

How do you play Lunatic Inquisition?

As a Villager, your goal is to survive until the timer ends. As a Courtier, your goal is to kill and convert all the Villagers.

Villagers have a secondary goal of completing the collection events in the four corners of the map. When completed, the events grant various feasts and helpful creatures. These events are also something to do while you wait out the clock.

Help, I'm stuck in the roof of the tower!

Yep! This is a known bug which happens a lot in Guild Wars 2. In my personal experience, about 1 out of every 3 times I load into Lunatic Inquisition, I'm stuck at the spawn point.

There is nothing you can do when this happens. Be sure to use your skills every so often, so that you don't get automatically kicked for inactivity. As long as you're waiting, why not file a bug report? Type /bug in the chat window and fill out the form to submit it.

Fortunately, even if you are stuck in the roof, you will still get credit for the daily when the timer ends.