Marinate the lamb: Combine the olive oil, lemon juice, garlic, paprika, cumin, oregano, red pepper flakes, 2 teaspoons salt and several grinds of black pepper in a medium bowl; whisk until smooth. Place the lamb on a rimmed baking sheet or in a roasting pan; poke about 10 slits into each side with the tip of a paring knife. Rub the marinade all over the lamb, massaging it into the meat and slits. Cover and refrigerate overnight.
Remove the lamb from the refrigerator and bring to room temperature about 1 hour before roasting. Preheat the oven to 350 degrees F and set a rack in a roasting pan. Wipe any excess marinade off the lamb and season all over with salt and pepper; transfer to the rack. Roast until a thermometer inserted into the thickest part registers 130 degrees F to 135 degrees F, about 1 hour 50 minutes. Remove from the oven, transfer to a cutting board and let rest 30 to 45 minutes before carving.
Meanwhile, make the mint sauce: Combine the mint, parsley, garlic, mustard, capers, lemon juice, sugar, red pepper flakes and 1/4 teaspoon salt in a blender and puree until smooth. With the machine running, slowly drizzle in the olive oil and blend until smooth. Transfer to a bowl. Carve the lamb and serve with the sauce.