Shutters
The first thing to note is that it seems difficult to move the lantern without injuring the machinery. The lantern is quite large, and attached to the ground via a metal stand. Let me make it clear that this object, while it looks very much like an obscenely large and complicated lantern, does not shed any light.
The shutters themselves seem resistant to your moving them. They seem to move somewhat independently. The only things that seem operable to you are the off/on switch, and the small door that opens into the lantern interior.
Inside the small door, it looks like some things are missing. There are three grooved slots on a rotating platform, currently empty. There is also what looks like a small empty metal vase in the very middle of the interior.
Thus your efforts to manipulate the lantern and the moths, while commendable, currently come to naught.