As you have had a good attempt I will give the answer. I believe part of the enjoyment of these sequences is working it out yourself and I have noticed a trend on itch io of people wanting everything spoonfed to them.
Clear Hint on end goal
What you need is lily stripped down to her underwear with a blindfold, gag, arms tied and crotch rope, then interact with the alter. The method to achieving these states is listed below
Stripping : While lily has cat ears interacting with a bear will strip lily of an item of clothing. there are 4 bears.
blindfold : Traveling through the hole in the wall will put a blindfold on lily. can be removed and put on by using it when arms are free
gag : sacrifice orb to alter. cannot be removed.
arms tied : Falling through the cracked floor will tie arms.
Crotch rope : there is a rope on the floor in the room with a hole in the wall. pick it up when lily is not a cat and use it from your inventory to tie a crotch rope.
Step by step instructions for if you are really stuck. (be warned the ending is not particularly satisfying).
there are a few orders you can do the steps in but a single mistake will force a reset
1) Cut arm binds off with knives on wall
2) go to hole room pick up rope and tie crotch tie.
3) go through hole in wall
4) get pickaxe.
5) pass gazer to the west and remove blindfold.
6) open north room.
7) go to north room and interact with note then curtains. (spawns bear)
8) in starting room interact with mirror, THEN PUT ON BLINDFOLD and finally pickaxe on mirror. (spawns bear).
9) pickup orb in north room.
10) go downstairs sacrifice pickaxe to alter. (spawns bear)
11) go to knife room use the knives to remove arm bindings
12) Pick up bottle and sacrifice it downstairs.
13) interact with both bears downstairs.
14) interract with one bear upstairs.
15) eat steak.
16) interact with final bear.
17) fall through cracked floor.
18) sacrifice orb to alter.
19) finally interact with alter to sacrifice lily to alter.
