Clean and prepare the fish fillets if needed.
Preheat the oven to 400°F (200°C).
Heat the olive oil and butter over medium-high heat in a large skillet. Add the fish.
Season lightly with salt and pepper. Brown on one side, then turn and brown the other side.
Remove the fish from the pan and place it on an oven-safe plate or baking dish. Transfer to the oven.
Bake until cooked through, about 5 to 10 minutes depending on the thickness of the fillets.
Reduce the stovetop heat to medium. Add the onion and cook until soft.
Add the garlic, capers, and anchovies. Cook, stirring regularly, until the anchovies break up, about 5 minutes.
Add the crushed tomatoes and 1 teaspoon lemon juice. Turn the heat to high and bring to a boil, stirring regularly. Cook until the tomato sauce thickens.
Return the fish to the pan and turn to coat with the sauce.
Garnish with fresh parsley and lemon slices.
