Begin marinating the lamb one day ahead.
Whisk mustard, vinegar, oil, garlic and brown sugar in medium bowl to blend. Place lamb in 13 x 9 x 2-inch glass baking dish. Spread marinade over each lamb rack. Cover dish with plastic wrap and refrigerate lamb overnight.
Preheat oven to 425°F. Transfer lamb to rimmed baking sheet; reserve marinade. Sprinkle lamb with salt and pepper. Roast lamb to desired doneness, basting occasionally with reserved marinade, about 25 minutes for medium-rare. Cut lamb between bones into chops. Divide chops among 4 plates and serve.