Fire up coals in a chimney.
While the coals are heating up, mix all the compound butter in a small bowl.
In the center of a plastic wrap, put the compound butter and wrap tightly both ends.
Place in the refrigerator meanwhile you are prepping the lobster.
Slice both lobsters lenghtwise, insterting the knife between both eyes first. This will instantly neutralize it's nervous system.
Put the hot coals under the cooking grates.
Melt about 2 tbsp of the compound butter and pour on the raw lobster meat.
Place the half lobsters, meat down, on the smoking grates.
After 5 minutes, turn the lobsters over, place a cube of compound butter on top and cook for another 3 minutes.