Preheat oven to 250 degrees F.
Pat the fish dry. Sprinkle the fish with 1 1/2 teaspoons salt and 1/2 teaspoon pepper and let stand 10 minutes at room temperature.
Chop half of the capers and mix with the unchopped capers. Arrange half of lemon slices in 1 layer in an 8-inch square glass baking dish and arrange fish fillets in a single layer over the lemon slices. Top with all of capers, remaining lemon slices, and 3 tablespoons parsley, then pour oil over fish. Bake in middle of oven, uncovered, until fish just flakes and is cooked through, about 1 to 1 1/4 hours.
Serve fish with some of lemon slices, capers, and oil spooned over. Sprinkle with remaining tablespoon parsley.