With kitchen shears or large sharp knife, cut each tail in half through center of hard topshell, meat of lobster tail, and through undershell. Set lobster aside.
In a small bowl combine 2 teaspoons of the lemon or lime juice, olive oil, garlic, and chili powder; brush on exposed lobster meat.
Grill lobster, meaty side down, on the rack of an uncovered grill directly over medium coals for 6 minutes, brush again with lemon mixture, turn and grill 6 to 8 minutes more or until meat is opaque in the center. Do not overcook.
Meanwhile, for dipping sauce, in a small bowl combine light mayonnaise or salad dressing, dillweed, lemon or lime peel, and remaining lemon or lime juice. Serve with dill sauce and fresh lemon or lime wedges, if desired. Garnish plate with fresh herb sprigs, if desired. Makes 4 servings.