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Remove necks and giblets and put into a large saucepan. Add onions, 2 carrots, 2 celery stalks, and the chicken stock. Bring to a boil over high heat and then reduce the heat and let simmer until reduced to about 2 cups. Strain and reserve; this is the turkey stock that you will use for the gravy.
Wash the turkeys, inside and out, and dry well. Coat inside and out with half of the olive oil. Season each turkey on the outside generously with the spice rub, pressing it in to adhere. Place 4 rosemary sprigs and 2 lemon halves inside the cavity of each turkey.
Arrange 4 of the halved carrots and 4 celery stalks on each of 2 half-sheet pans or baking sheets. Position each turkey on top of the carrots and celery so that the turkey does not rest directly on the bottom of the pan. Drizzle turkeys with remaining olive oil.
Roast until an instant-read thermometer (inserted deep into the thigh but away from the bone) reads 165 degrees F and juices in the thigh run clear when pierced with a fork, about 2 to 2 1/2 hours; begin checking at 2 hours. Remove from the pans and let rest for 15 minutes before carving. Reserve pan juices for gravy.
While turkeys are resting, make the gravy. In a medium heavy saucepan, cook flour and butter over medium heat for 3 to 4 minutes, or until a blond roux is formed. Add pan juices and then reserved turkey stock and bring to a boil over high heat. Reduce the heat and let simmer until thickened and ready to serve.
Carve turkey as desired and serve with gravy.