Preheat the oven to 400 degrees F.
Line a heavy large baking sheet with foil. Oil the foil and fish with 1 tablespoon of oil. Place the fish atop the foil. Sprinkle the fish cavity with salt and pepper. Squeeze 1/2 of the lemon inside the fish cavity. Fill the cavity with the onion, fennel and rosemary sprigs. Bake until the fish is just cooked through at the bone, about 40 minutes.
Meanwhile, squeeze the remaining lemon 1/2 into a small bowl. Whisk in the fennel fronds, rosemary, and garlic. Gradually whisk in the remaining 3 tablespoons of oil. Season the lemon sauce, to taste, with salt and pepper.
Using a sharp knife, separate the 2 fillets from the backbone. Using a metal spatula, transfer the top fillets to a plate. Lift the fish backbone from the bottom fillets (the backbone and head should come off together easily), and discard. Using the spatula, transfer the remaining fillets to plates. Sprinkle the fish with salt and pepper. Drizzle the lemon sauce over the fish and serve.