Method
Set each lobster tail with the translucent membrane down and curved shell facing up. With shears or a heavy, sharp knife cut through the curved shell and meat, leaving the membrane intact. Open the tail gently like a book so its hinged in the center. Pour 1/2 tsp of the olive oil over each tail; season lightly with salt and pepper. Place the lobster meat-side up over a medium-hot fire and grill until opaque, 8 to 10 minutes, turning once.
Note: If using live American lobsters, kill them immediately before cooking. Remove the stomach and discard; remove the claws and legs and reserve; split the tail as directed. Place claws, legs and body on grill over a medium-hot fire and cover with foil. Place the tail meat-side up. Grill until the shells are bright red, turning the claws and tail once. Grill the legs 4 to 6 minutes, claws about 8 minutes, tail and body 8 - 10 minutes. If frozen, thaw the lobster in the refrigerator overnight.