After Aethelmaer discovers a button with a lily sigil on the victim, he suggests asking Miounne if she recognizes it.
This quest is available if you have completed the quest Power of Deduction.
Show the Lily Button to Miounne
Go back to Gridania and go to the Carline Canopy, which is south of the Gridania Aetheryte Plaza, and talk to Miounne. Hand over the button.
Show the Lily Button to Bernadette
Leave the building and go north to the aetheryte plaza, and talk to Bernadette. Hand over the button.
Show the Lily Button to Ceinguled
Use the Aetheryte to go to the Lancer's Guild, or if you haven't added it to your list of destinations yet, go northeast to the exit to Old Gridania, then go north until you are close to the quest destination, and turn left to find the Lancer's Guild aetheryte to attune to it before you proceed.
Go to the Lancer's Guild and talk to Ceinguled to hand over the button.
Show the Lily Button to Ursandel
Go northwest to the quest destination and talk to Ursandel, then hand over the button to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Ursandel to accept the next quest: Skeletons in Her Closet. There will be a cutscene.