Use the oil to grease a shallow baking dish that is large enough to fit the fillets in a single layer. Arrange the fish in the dish and turn to coat with the oil. Sprinkle with the lemon juice, oregano, salt, and pepper. Dot with the butter and cover with foil.
Bake until the flesh is cooked through but still very juicy, 20 to 24 minutes. Serve topped with the pan juices and parsley (if using).