Lobsters are generally split in half lengthwise for grilling to gain flavor from the grill.
After you split the lobster, remove the stomach (which is found in the head area) and the intestine (a small clear or black tube running the length of the lobster), if you find it. Twist the claws and legs from the body and keep separate for steaming. The claw shell, which is softer before being cooked, can be cut on one side with a large knife. This will alleviate the need to crack them at the table.
Because lobster meat breaks down or spoils rapidly once the lobster is dead, they are most often split just before grilling. If you are unable to kill and split the lobsters yourself, have the market do it for you no more than 4 to 6 hours in advance and keep the lobsters well iced until you are ready to cook them.