Here is the full list of all 41 The Lamplighters League achievements.
Meet Locke at the Hideout
Stabilize an Agent in Mortal Danger
Recruit the Alexandrite
Recruit Ana Sofía
Recruit Célestine
Recruit Fedir
Recruit Jianyi
Recruit Judith
Recruit Purnima
Recruit Mother Amina
Recruit Danys Belfort
Recruit Madame Mei
Recruit the base 10 Agents in a single campaign
Deal a total of 10000 damage across all Agents
Learn the truth about the Houses of the Banished Court
Complete the Campaign
Complete the Campaign on Survivor Mode
Completely unlock any Agent's Skill Tree
Unlock a Tempered Weapon
Defeat Trace Marteau in a non-Critical Mission
Defeat Lady Nicastro in a non-Critical Mission
Defeat Lord Strum in a non-Critical Mission
Complete the Marteau Heist, "The Other Side"
Complete the Nicastro Heist, "The Cold Epiphany"
Complete the Strum Heist, "Tomb of the Everlasting"
Upgrade any Undrawn Hand Card to Level III
Upgrade any Undrawn Hand Card to Level V
Remove a Breaking Card by taking the affected Agent on a Mission
Complete an Assassination.
Destroy a Crossroads Beacon.
Equip an Agent by filling all 6 Item Slots
Defeat a total of 100 monsters
Complete a Mission successfully with Ingrid and Fedir in your squad
Complete a Mission successfully with Lateef and Judith in your squad
Complete a Mission successfully with Eddie and Purnima in your squad
Complete a Mission successfully with Célestine and Ana Sofía in your squad
Complete a Mission successfully with Célestine and Alexandrite in your squad
Complete a Mission successfully with Ana Sofía and Jianyi in your squad
Complete a Mission successfully with Fedir and Judith in your squad
Complete a Mission successfully with Fedir and Purnima in your squad
Defeat Lady Nicastro in the Tutorial mission "A Hasty Escape"