The Lobster Trap is an item in Big Nate Island that you will give to the Sailor and he will give you another item that will be useful.
How to get the Lobster Trap
Run all the way to the lighthouse. Walk out onto the dock and put on your Scuba gear. Then jump into the water and click when your cursor says Dive. You’ll be underwater and you have only a little bit of oxygen so you need to move really fast. Just swim all the way to the right and then go straight down. Pick up the lobster trap on the ocean floor and let your oxygen run out. You’ll re-appear at the start and then you just need to swim back up to the dock.