Hello, I am a little late to this discussion but I just did this part of the game for the first time last night.
Firstly, did you complete the quest for helping the cook wash dishes? I did this after over an hour of scouring the castle grounds and once I completed it, upon leaving and returning to the castle, the cat appeared in the hallway between Lela's room and the kitchen.
I don't know if this is exactly a prerequisite but its what happened in my game.
I hope this helps!
