Well, the issue with all of this is that dialogue options (and not talking with them ) influences Fear and Suspicion. Apparently staying up late also influences Suspicion.
I will ask if you do somehow get Lily to leave due to fear, take note of which dialogue options you took with her, what you did in front of her, and how often you stayed up. With that, I should be able to theoretically figure out the rest.
I tried my usual stuff with the cast and eating all the bread, I still lose Lily at the end due to fear, no matter what I do.
ROUTE SPOILER.
*Be sure to always talk to each character at least once.
>D1
Morn: Rite. Oil. Bitter
Day: Enter ALICE's room.
Night: Berries on ALICE.
>D2
Morn: Keys. Lotion. Wine.
Day: Incense.
Night: Eat all the Bread.
>D3
Morn: Place Rite.
Day: Nothing.
Night: Oil JUDIE. Watch SARAH read the scrolls.
>D4
Morn: Necklace. Plant Necklace.
Day: Nothing
Night: Lotion MINERVA. (Incense LILY for regular win.)
>D5
Morn: Lotion KATHERINE.
Day: Nothing.
Night: Nothing.
>D6
Regular Win if LILY was incense'd, otherwise Fear Loss.