Holmes' quote, "I was born with the devil in me," is an actual quote attributed to the real H. H. Holmes when he confessed to his murders.
Pat Quinlan was a caretaker for the real H. H. Holmes. He claimed that he had no knowledge of the murders and wasn't allowed to clean the second floor "trap" rooms.
Abigail Spencer (Lucy) is good friends with Meghan Markle, and was at her wedding to Prince Harry. Markle is actually distantly related to the real H. H. Holmes (Herman Mudget). Both are related to Thomas Mudget and his wife, who were born in the 1600s.
Upon entering the World's Fair Hotel, you can see 603 as the address. This may be a nod to the fact that H. H. Holmes was born in Gilmanton, New Hampshire, which has the area code 603.
When Lucy is talking to Harry Houdini, she mentions the "cutpurse". The cutpurse is not an act, but rather an archaic reference to pickpocketing.