Heat your grill to medium-high. Brush steaks lightly with olive oil; season with salt and pepper. Cut each lobster tail lengthwise in half. Pull out the meat and cut into ½" to 1" pieces.
Grill steaks to the desired doneness, allowing 2 to 3 minutes per side for rare, and 3 to 4 minutes per side for medium rare to medium. While the steaks cook, melt the butter in a skillet set over medium to medium-high heat. Add the lobster and sauté 3 to 4 minutes, until just cooked through. Add the lemon juice, cayenne, garlic and parsley.
When cooked, plate the steaks, top with the lobster mixture, and serve.