Does this box in the movie 妖猫传 (Legend of the Demon Cat) say 鳳栖樓 on its lid and 私人必死 inside, and what do they mean?
Never saw the movie.

鳳栖樓 should be the name of the building. You are mentioning there is a key in the box, so it is probably the building where the key is for.

As the note inside the box, you got one character wrong. It is "私入必死", where 入(ru4) means "enter".

Here, 私 means "without permission". So the whole phrase is saying the "(you) will definitely die if enter without permission"

入 and 人 look alike, but are two totally different characters.