Remove turkey from refrigerator one hour before roasting. Remove the neck and giblets from the turkey, rinse it well, and pat with paper towels until it is very dry. Place on a cooling rack so that air circulates and let sit uncovered to further dry the skin.
Preheat the oven to 350°F. Place the carrots in a roasting pan.
Zest and juice one of the lemons. Coarsely chop 2 tablespoons of thyme leaves. Combine the lemon zest and juice and chopped thyme with the butter.
Season the cavity of the turkey with salt and pepper. Quarter the remaining lemon and loosely stuff along with the orange, onions, rest of the thyme, and garlic.
Working from the neck end, slide your fingers under the skin until you reach the end of the breast, being careful not to tear the skin; rub about half the citrus herb butter under the skin. Smear the remaining butter all over the outside of the turkey. Season with salt and pepper.
Tie the legs together with kitchen string and tuck the wings underneath the bird. Place the turkey breast side up on the carrots in the roasting pan.
Place the turkey in the oven and roast for 2½ - 3 hours (13 minutes per pound) or until the juices run clear and the internal temperature is 165°F.
Remove the turkey from the pan, tent loosely with foil, and allow to rest for 30 minutes before carving.