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.
Marine Cages are crafted at the Smithy. They require Iron Ore.
Iron Ore can be found in the Smugglers’ Cave. The more Guides and Guests you send to the cave, the better chance you’ll have to get Iron Ore. You can send a total of four visitors.