Speak with Tarquin and decide to kill him or leave him. There are many things to loot here, including many Empty Potion Bottles you can use to craft potions. Pick up the Dusty Tome in Dallis' cabin and read it to learn the tune (On her desk). To open Port-Side Stateroom Door you need the password ('Fortitude') and the Strange Gem. Alternatively, search the corpse on the deck by the dead Gheist and read through the journal called sodden diary. Find the Starboard Stateroom Door and try to open it by telling it you forget the password and need a reminder. You can either Persuade Magister Renly to let you or you can kill her and then take it. Head to Bishop Alexandar down one more deck, inspect him (by attempting to 'talk' with him) and take the Strange Gem.
Head below deck and if you have Pet Pal skill, the rat on board will tell you this ship is controlled by singing songs.
Find a way to get the Lady Vengeance moving. Lady o' War is a Quest in Divinity: Original Sin II.
