From Nookipedia, the Animal Crossing wiki
The Lantern Fly (ビワハゴロモ. Biwahagoromo) is an insect found on trees between June and September at two different times of the evening, between 4 p.m. to 7 p.m., then again from 11 p.m. to 8 a.m.. It is uncommon and can be found in the rain as well as on clear evenings.
Donating to the museum
In Wild World
"The lantern fly drinks the sap of the lychee, whose fluids are said to be sweet. ...The question is, who first sampled the lychee, anyhoo? It looks repellant! It took a gourmand braver than I, I assure you!"
In City Folk
"It's said that a diet of sap from the lychee tree makes the bodily fluids of the lantern fly sweet. It's also said the proper way to try them is to break off the tips of the horns and sip them like straws... It's ALSO said that anyone who does those things is officially googly-boogly out of his or her mind."
The Lantern Fly can be found in the top-most level of the insect section of the museum, perched on the right-most cedar tree, next to the sign.
In New Leaf
Upon being donated, the Lantern Fly can be found in the room of the bug exhibit with the light in, resting on a tree near the light. The exhibit has this to say about the Lantern Fly:
"Lantern flies stay on trees to drink tree sap, which is where you'll most commonly find them. Their heads are shaped like alligators, though this is just an odd coincidence. Their wings have patterns that look like eyes so when they're open they can scare off predators. They don't really cry that much, but they are still related to cicadas to some extent. "
"With alligator-like heads and mothlike wings, these are actually cicadas."
Fulgora laternaria (also known as Lantern Fly, Alligator Bug, Peanut Bug, etc.) is related to cicadas. It gets the name 'lantern fly' and 'alligator bug' from its oddly shaped and colored head. Its head is shaped like a serpent or lizard, similar to an alligator's head, which is mentioned in the description in the Bugs and Fish tab. The name 'lantern fly' however, comes from the mistaken belief, first by Carl Linnaeus, that they are luminescent. It protects itself by opening its wings, which reveals fake eyes. Its head may also further protect itself, by scaring potential predators. In the game, it displays its wings when the player gets close to it.
Names in other languages