Remove giblets and neck from turkey, and rinse turkey with cold water. Drain cavity well; pat dry. Rub 4 Tbsp. Citrus-Salt Rub into cavity. Rub skin with remaining rub. Cover and chill 18 to 24 hours.
Preheat oven to 350°. Rinse turkey; drain cavity well, and pat dry. Toss together lemons, next 6 ingredients, 1/4 cup olive oil, 3 Tbsp. lemon juice, and 1 tsp. salt in a large bowl; spoon mixture into cavity of turkey.
Tie ends of legs together with kitchen string; tuck wingtips under. Place turkey, breast side up, on a lightly greased roasting rack in a large roasting pan.
Whisk together orange juice and remaining 3 Tbsp. lemon juice and 1/2 tsp. salt in a bowl; gradually whisk in remaining 1/4 cup oil until blended. Brush half of orange juice mixture over turkey.
Bake at 350° on lowest oven rack 1 hour. Brush remaining orange juice mixture over turkey, and bake 45 more minutes. Pour 1 cup broth into pan; bake 45 minutes. Pour remaining 1 cup broth into pan; bake 45 more minutes or until a meat thermometer inserted into thickest portion of thigh registers 165°. Remove from oven, reserving pan juices. Cover loosely with foil; let stand 30 minutes. Transfer to a platter; serve with pan juices and Lemon Aïoli.