Grilling a lobster gives it a different flavour to boiling, and allows you to introduce other flavours during the cooking process (over say, boiling). You can use any sort of grill for this. If you don't have a grill, you can bake it instead.
I usually baste the lobster while it's cooking with butter to get a nice colour on the meat. Avoid using garlic or anything that may easily burn while grilling the meat (you can cover it in this after grilling).
If you've overcooked the lobster, the claw meat will stick to the claws when you're trying to get the meat out.