Nothing particularly interesting, I'm afraid. The liquor cabinet key, as Nishitani-san has guessed, and three bedroom keys.

[She kinda sighs at the last part. Oh the perks of roommates dying... or so.]

Alright, so whatever this key opens it's not in the library. If it turns out that this key was a red herring to get us to waste our time, I suppose the Sage played it well.