Preheat barbecue to 400°F (205°C).
To prepare sauce, combine mustard and water in a small bowl; whisk well. Stir in remaining ingredients. Set aside.
To prepare lobster, make a lengthwise cut through the top of each lobster shell using kitchen shears, cutting to, but not through, lobster meat. Press shell open. Place the lobster tails, cut sides up, on a hot barbecue. Combine oils and pepper, and spoon over the lobster meat.
Close barbecue lid and cook for 13 minutes or until the lobster meat turns opaque. Serve lobster with sauce, and garnish with onions, if desired.
Makes 2 servings of 1 lobster tail, each with 2 tbsp (30 mL) dipping sauce.