Lyse remembers one of the people from Hancock's list whom she hasn't spoken to yet.
This quest is available if you have completed the quest A Good Samurai is Hard to Find.
Starting the Quest
Talk to Lyse in Kugane to begin the quest.
Speak with Gyodo
Go up the stairs that spiral around the inside of the building until you find Gyodo at the quest icon on the map. Talk to Gyodo and there will be a cutscene.
Speak with Alphinaud
Go downstairs and exit the building, and use the nearest Aethernet Shard or the main Kugane Aetheryte to go to the Ruby Bazaar Aethernet Shard. Enter the building and talk to the East Aldenard Trading Company Aide, and say Yes to enter the Ruby Bazaar offices. Talk to Alphinaud and there will be a cutscene.
Speak with Alisaie
Talk to Alisaie to proceed.
Wait with Alisaie and Lyse
Go outside and use the Aethernet Shard to go to the Shiokaze Hostelry Aethernet Shard. Enter the Shiokaze Hostelry and go up the stairs that spiral around the inside of the building until you find a door in the south wall. Go through the door and go to the quest icon on the map. There will be a glow around Alisaie, indicating an instanced battle. Check on her and there will be a cutscene, and then the battle will ensue.
Solo Duty: It's Probably a Trap
Defeat any enemies that are attacking you directly, starting with one of the Imperial Princeps. After you defeat it, if the other Imperial Princeps is still attacking you directly, defeat it next; otherwise, defeat the Imperial Centurion that is attacking you directly. After that, defeat any remaining enemies.
Afterward, there will be a cutscene.
Next, you need to avoid being seen by the Sekiseigumi. Do not attack them or you will fail the duty. Early on, you will be caught by a couple of Sekiseigumi. This is unavoidable. Wait for Lyse to tell you to use a Smoke Bomb; this will unlock the Smoke Bomb Duty Action. Use the Smoke Bomb Duty Action to become transparent and escape from the Sekiseigumi's chain, then go partway around the building, just far enough to stay out of their sight.
Note that the Smoke Bombs make you transparent for a short time, so you can use them for stealth, not just for escape, so be sure to use Smoke Bombs often.
After you escape the first Sekiseigumi's chain, go northeast, then try to reach the stone stairs to the east. You can use a Smoke Bomb to become transparent and then go past any Sekiseigumi in the way.
There are three eastward paths that you can take from there. The leftmost path is recommended. Use Smoke Bombs whenever you need to become transparent and go past the Sekiseigumi.
Continue going east, and go up the stone stairs at the end. A Curious Kojin will appear. At this point, just follow the Curious Kojin. Eventually, there will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Speak with Lyse
Talk to Lyse to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Lyse to accept the next quest: Making the Catfish Sing. There will be a cutscene.