The meat of the lobster is found within the tail, while the legs have some, more than 90+% is found in the tail. Grabbing the tail and the non-tail section (carapace), simply twist to separate the two sections. Pull out the vein and the lobster is ready to cook. Grilling a whole lobster (with head on) makes an appealing dish, but really only takes up more grill space. For the grill — split the tail lengthwise — add some olive oil, garlic and butter!
While it depends on the size, start with cooking for about 1 minute, meat side down, which adds some nice grill marks across the meat. Flip, add more olive oil and garlic and cook for another 6 minutes, shell side down.