Combine lime juice, 2 tablespoons cilantro, and oil in a large shallow dish. Place grouper in dish, turning to coat. Cover and marinate in refrigerator 20 minutes, turning once.
Remove fillets from marinade, discarding marinade. Sprinkle with salt and pepper. Place fillets in a grilling basket coated with cooking spray.
Coat grill rack with cooking spray and place on grill over medium-hot coals (350° to 400°). Place basket on rack; grill, uncovered, 10 minutes on each side or until fish flakes easily when tested with a fork.
Transfer grouper to a serving platter, and top evenly with Tomato- Papaya Salsa. Sprinkle with remaining 2 tablespoons cilantro.