Flower
The glass flower from the crypt is the perfect size for the lantern. Once in place with the door shut, the random rotation of the shutters causes strange, almost ghostly white light to stream throughout the theatre. On a WI check, you'd notice that the mechanical moths seem slightly attracted towards the new light source, but still focus on the top of the theatre.
The light coin doesn't seem to fit anywhere, although it too would cause light to emit from the lantern, obviously.
You cannot find any glass panes that fit in the lantern grooves.