Remove the turkey giblets from the cavity and rinse the turkey well. Pat dry and put it on a roasting rack in a roasting pan. Salt the turkey cavity and squeeze the juice of the lemons inside the cavity. Stuff the cavity with the lemon halves, rosemary and 2 onion quarters. Add the remaining onion, all of the giblets and turkey parts, and 4 cups water to the bottom of the roasting pan. Season the skin of the turkey with salt and pepper, to taste, and rub with butter. Put the turkey in the oven and roast until the temperature of the breast reaches 170 degrees F on an instant-read thermometer, 3 1/2 to 4 hours. Baste the turkey with pan juices every 30 minutes. Cover with foil if browning too fast.
Remove the turkey to a cutting board when ready and allow it to rest for 20 to 30 minutes before carving. Arrange the carved turkey on a serving platter and gobble it up!