Then, you can do two things: either you par-cook the claws and tail before grilling, or place them directly on the grill. If you cook the meat before, she says that you have more control over the cooking and will still get some nice grill marks on it. Placing them raw on the grill means you have less control over how it's cooked.
To par-cook them, she says to cook the claws almost all the way (about 7 minutes for a 1 ½ pound lobster), place in an ice bath to stop the cooking, remove the meat from the shell, and then throw them on the grill of a couple of minutes so they heat up and gets some grill marks. The tail should be cooked for about 4 minutes for a 1 ½ pound lobster (until opaque, but not completely cooked), placed in an ice bath, then split in half lengthwise, and placed on the grill for a couple of minutes.
To cook them directly on the grill, remove the claw from the shell, and split the tail in half. Place both pieces on the grill until opaque and cooked through.