Here is the full list of all 41 Lamplight City achievements.
Every friendship has one
Played through the entire game without opening the casebook
Checked yourself into Riverview Asylum
Declared a case unsolvable
You're so annoying
Found every single clue and document in the game
Correctly solved every case
Confronted the Justice Killer in his own home
Sang a popular drinking song
Eavesdropped on every conversation
Completed the game
Ended up in jail
Told Adelaide the truth
Accused Tom Puffin of murdering Ronan L'Espaye
Accused Jimbo of murdering Ronan L'Espaye
Discovered the truth about the cooping scheme
Read every book in the game
You voted!
Told Patrick a story
Accused Roger DeVay of murdering Desiree Lathan
Accused Margaret Andrews of murdering Desiree Lathan
Concluded that Desiree Lathan's death was due to spontaneous human combustion
Gave Charlotte Robineaux a music lesson
Tricked Jonas Usher
Showed Desiree's ashes to someone who wasn't Dr. Edwards
Successfully located Linda Walker
Accuse Linda Walker of kidnapping the Harris baby
Accused Malcolm Harris of kidnapping his own son
Accuse Arthur Devins of kidnapping the Harris baby
Fixed the boiler without any help
Told Angela Maxwell about your problems
Spoke with Roland Deveraux
Learned about Mrs. Davis's hobby
Accused Albert Martin of Madame DuPrée's attempted murder
Got kicked out of Sabine Martin's apartment
Revealed Madame DuPrée's true nature
Accused Juliette Montgomery of Madame DuPrée's attempted murder
Accused Guy Dumas of Madame DuPrée's attempted murder
Played a familiar melody
Read Madame DuPrée's poems
Kept your promise to Mrs. Hanbrook