In a small bowl, whisk together the butter, lemon juice, garlic, sea salt & Old Bay seasoning. Set aside for later.Turn the lobster tails upside down and use kitchen shears to cut lengthwise through the centers of the soft undercover of the tails.
Preheat a grill to medium-high heat.With the cut side up, brush lobster meat with the cooking oil.Place the tails cut side down on the heated grill for 6 minutes, until the top of the shell is bright red.