This is one time when I would puncture the skull to kill the lobster before cooking. The grill would not kill the lobster fast enough.
I would prefer boiling the lobster, stuffing the body with crab meat and broiling for a finish.
'La bonne cuisine est la base du véritable bonheur.' - Auguste Escoffier
(Good food is the foundation of genuine happiness.)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)