Preheat oven to 450°F. In a large, heavy roasting pan, toss together onion, 1 Tbsp. olive oil and garlic. Top with parsley, rosemary sprigs and thyme sprigs. Place lamb on herb sprigs. In a small bowl, mix together remaining 2 Tbsp. oil, chopped rosemary and chopped thyme; season with salt and pepper. Coat lamb with mixture.
Roast lamb for 15 minutes; reduce oven temperature to 350°F and roast, basting every 15 minutes, until a meat thermometer inserted in thickest part of meat away from bone registers 145°F for medium-rare, 1 hour and 15 minutes to 2 hours.
Make mint sauce: Coarsely chop mint. Transfer to a bowl and stir in vinegar.
Let lamb rest, covered with foil, for 15 minutes. Carve lamb and serve with mint sauce.