Heat oven to 400° F.
Season the lamb with 1 teaspoon salt and 1/2 teaspoon pepper. Place the lamb in a roasting pan.
In a small bowl, combine the garlic, tarragon, and 1 tablespoon of the oil. Rub over the lamb and roast, 25 to 30 minutes for medium-rare (internal temperature 125&#!76; F). Transfer to a cutting board and let rest for 5 minutes before slicing.
Meanwhile, heat the remaining oil in a skillet over medium-high heat. Add the onion and cook until soft, about 4 minutes. Add the beans, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook, stirring, until heated through, 3 to 4 minutes. Serve with the lamb.