Rub tenderloin with oil, salt, and pepper. Place carrot and onion in bottom of a shallow roasting pan. Place tenderloin on vegetables. Tuck narrow end under to make roast more uniformly thick. Pour lemon juice over tenderloin; cover and marinate at least 3 hours.
Pour broth into pan; insert meat thermometer in tenderloin, if desired. Bake, uncovered, at 500° for 5 minutes; reduce heat, and continue baking, uncovered, at 350° for 55 minutes or until thermometer registers 140° (rare). Cut into thin slices.