You can store live lobsters 24-36 hours in your refrigerator before cooking. Remove from its store packaging, set in a large container and completely cover with a damp cloth(s). Ensure that the cloth stays damp the entire time the lobsters are stored. Never store live lobster on ice or in fresh water.
To grill a live lobster, use a long, sharp knife to split the lobster in half lengthwise. Scoop out the innards. Brush lobster with garlic-and lemon-flavoured melted butter; season with salt and pepper. Grill, flesh side down, over medium-high heat, 3 minutes. Turn over and brush with a little more flavoured butter. Cook 4 to 5 minutes more, or until cooked through.