Preheat oven to 425 degrees. Season lamb with salt and pepper. Heat a large skillet over high heat. Add 1 tablespoon oil. Sear lamb on both sides until deeply golden, 4 to 5 minutes.
Transfer racks to a rimmed baking sheet, fat side up. Toss potatoes with 2 tablespoons oil, and season with salt and pepper. Arrange potatoes around lamb.
Roast until an instant-read thermometer inserted into the center of the lamb reaches 130 degrees (medium-rare), 20 to 25 minutes. Transfer racks to a cutting board. Return potatoes to oven. Roast until tender, about 15 minutes more.
Combine remaining 1/2 cup oil, the parsley, shallot, vinegar, oregano, garlic, orange zest and juice, red-pepper flakes, and 1/2 teaspoon salt. Spoon some sauce over lamb. Carve lamb into individual chops, slicing between ribs. Serve with potatoes and remaining sauce.