Preheat the oven to 350 degrees F. Let the turkey sit at room temperature, covered, for 30 minutes to come to temperature before preparing.
Zest and juice the lemon, lime and orange. Reserve the juice for another use and set the rinds aside. Mix the butter with the citrus zest and salt and pepper to taste. Rub the seasoned butter all over the turkey, inside and out, as well as under the skin. Put the citrus rinds and leeks into the cavity. Tie up the legs and put the turkey, breast-side up, onto the rack in a roasting pan. Pour 2 cups water into the pan and roast, basting with the pan juices every 15 to 20 minutes. Cook until the internal temperature taken from the thickest part of the thigh is 170 degrees F, 15 to 20 minutes per pound. Remove the turkey from the oven and let it rest for 20 minutes before carving. Reserve about 1 1/2 cups turkey and 1/2 cup of the pan drippings for another use if desired, such as the Round 2 Recipe Thanksgiving Pie.