Purchase Lobsters in the Island Store under the Animals tab. You’ll receive a Lobster Trap to place in the water.
When you tap on the floating Lobster Trap, you’ll see an icon for Marine Cages. Drag a cage onto the trap and come back later to collect Lobsters. As with other animals, you can use one more Marine Cages. The more cages you use, the longer it will take to collect, but the more Lobsters you’ll get.