The recipe for the potion to handle a Lilyth, as well as a pair of correct numbers to search the bookshelf for, are located through a portal that will appear once you complete the festival of life or otherwise make it rain. Page 8 of the journal contains an almost correct recipe for True Sight. You do need to eat the mushrooms to get True Sight, brewing them does nothing but waste them.
The Library Key is located within Lady Jessica’s room.
Spoilers
The recipe for True Sight is Echoshroom, Mind Sap, and Death’s Candle. To enter Lady Jessica’s room you will (possibly) need a light source and her outfit from one of the chests on the East Wing of the manor. You will likely encounter the mimic chest which will prevent you for changing your outfit. The mimic dress can be stripped by the upstairs hallway wind trap. Once you are wearing her outfit enter the room in the upper right side of the East Wing near the Library. Go south until you get possessed by the red ghost. Go to Lady Jessica’s door and it will unlock itself and let you enter. Normally, I’d wait here until the possession expires but the mirror trap will always trigger in my experience when you pass by the mirror in the bathroom to pick up the Library Key in the bathtub.