Start the Z Grills on the smoke setting, lid open,until the fire is established (4-5 minutes). Turn temperature to 450 °F and preheat, lid closed, for 10 to 15 minutes.
Combine butter, lemon juice, garlic, salt,and pepper. Cook on the grill for 5-10 minutes or until butter melts. Reserve half of the butter for serving.
While butter is melting, prepare lobster tails. Cut down the top of the shell and expose lobster meat. Brush lobster meat with butter mixture.
Place lobster tails on the grill and cook for approximately 15 minutes. Halfway through cook time, brush again with butter mixture.
Serve with reserved butter. Enjoy!