Although fish is often grilled over indirect heat, we prefer cooking whole snapper over moderate direct heat.
Prepare grill to medium heat.
To prepare sauce, combine the first 10 ingredients; set aside.
To prepare fish, score each fish with 3 diagonal cuts on both sides. Brush outside of fish evenly with olive oil. Sprinkle with kosher salt and black pepper. Stuff lemon and garlic slices into cuts. Place any remaining lemon slices into each fish cavity. Coat outside of fish with cooking spray.
Place fish on grill rack; grill 40 minutes or until fish flakes easily when tested with a fork. (Fish does not need to be turned.) Serve fish with sauce.