Preheat your grill: Start by preheating your grill to medium-high heat (about 400-450°F). This ensures that the seafood gets a good sear while cooking evenly.
Prepare the lobster tails: Use kitchen scissors to cut the top of the lobster shell lengthwise, stopping just before the tail. Carefully lift the meat from the shell, leaving it attached at the tail end for presentation. Set aside.
Pat the shrimp dry: Rinse the large shrimp under cold water and thoroughly pat them dry with paper towels. This will help achieve better grilling results.
Make the marinade: In a mixing bowl, combine 4 tbsp melted unsalted butter, 4 tbsp olive oil, 4 cloves minced garlic, 2 tbsp fresh lemon juice, 1 tbsp chopped fresh parsley, 1 tsp paprika, 1/2 tsp salt, and 1/2 tsp black pepper. Whisk everything together until well blended.
Brush the lobster and shrimp: With a pastry brush, generously coat the prepared lobster tails and raw shrimp with the marinade. Ensuring each piece is well covered will infuse them with incredible flavor.
Grill the lobster: Place the lobster tails on the grill, meat side up. Grill for 10-12 minutes, until the meat is opaque and cooked through (it should reach an internal temperature of 145°F).
Add the shrimp: During the last 5 minutes of grilling, add the shrimp to the grill. Grill until they turn pink and opaque, which usually takes about 3-5 minutes depending on their size.
Serve: Once cooked, remove the lobster and shrimp from the grill. Arrange them on a serving platter, drizzle with any remaining marinade, and garnish with additional parsley. Serve with lemon wedges for that refreshing zest!