From Nookipedia, the Animal Crossing wiki
The Lobster (ロブスター, Robusutā) is a rare crustacean which can be found in the ocean all day between November and February. It is sold for 2,500 Bells. In the "Bugs and Fish" window in City Folk, it has the description: "These are the créme de la créme of the shrimp group." It is suggested that the Lobster in Animal Crossing: City Folk is a Maine Lobster. Its shadow size is about the same size as the Sea Bass.
Donating to the Museum
Like all fish and bugs in the Animal Crossing series series, the Lobster can be donated to the Museum by talking to Blathers, the curator. Upon donating, he will tell the player a bit of information about the Lobster.
In City Folk
Upon donating to the Museum in Animal Crossing: City Folk, Blathers will say;
"Lobsters rather remind me of shrimp, though many call them crawfish of the sea. Size varies by species, but some lobsters have been known to grow to a massive 120 centimeters (48 inches) in length. ...I rather dislike them, actually. Their clicky legs and vile bellies call insects to mind, I'm afraid."
The Lobster can be found in the back tank, crawling on the bottom.
In New Leaf
The Lobster is now classed as a deep sea creature rather than a fish, meaning that it is no longer caught by using a fishing rod; rather, the player must dive underwater once they have obtained a wet suit. After being donated, it can be found in the large pool in the first room of the Ocean exhibit. The exhibit has this to say about the Lobster:
"Lobsters live in the ocean, have large, powerful claws, and are closely related to crawfish. They are a delicacy, also known by the names "crawfish of the sea" or "homard," their French name. However, unlike crawfish, they are much bigger and can live for more than a hundred years. Lobsters are aggressive and will pinch with their claws if you don't properly bind them while handling."
In City Folk
Lobsters are invertebrates and can be found all over the world. They have an exoskeleton which protects them from predators, which they molt in order to grow, making them incredibly vulnerable at this point of time. They live in rocky areas under the sea, which also helps them to protect themselves from predators. Lobsters come in different forms, clawless and clawed but they all have ten legs (the claws on clawed lobsters are adapted to be legs). Lobsters can be known to live up to one hundred years.