In order to complete the puzzles in Cassandra’s Room, you need to have gotten the Medicine Box Key from the Grand Parlor and unlocked the Medicine Box in Lottie’s Room (Orderly room on the map). That will give you Dr. Jenkins Lozenges.
Medicine Bottle Puzzle
On the desk in Cassandra’s Room is Margrave Liniment. Add that to your inventory as well and then you can put both of those on the tray with the existing two. Then you need to order them so that the rot line connects from bottle to bottle.
Notice that 3 of the bottles have numbers on them. 2 – 5 – nothing – 7. We’re going to use the Zodiac picture from Elisabetta Perosi’s Journal to translate those to Pisces, Gemini, and Leo.
Now you can use that to unlock the zodiac lock.