Preheat your grill to medium-high.
Set an oven rack 6” beneath the broiler. Preheat the broiler to high heat.
Cut each lobster tail in half lengthwise. Place the half lobster tails, flesh side up, in a single layer in a small, shallow baking dish.
Combine the butter, lemon juice and cayenne in a small bowl. Brush this mixture on the flesh of each half lobster tail.
Brush the steaks lightly with the olive oil;
season with salt and pepper. Grill the steaks to the desired doneness, allowing, approximately
2 to 3 minute per side for rare, and 3 to 4 per side for medium rare to medium.
Set the steaks on a plate, tent with foil and set on the stovetop until the lobster tails are ready. Broil the lobster tails for 4 minutes, or until just cooked through. To serve, place one steak and two half lobster tails on each of 2 plates.