Bring 6 1/2 quarts water to a boil. Remove from heat and add tea, lemon peel and rosemary. Cover and let steep for 20 minutes. If using tea bags, remove them. If using bulk tea, remove lemon peel and rosemary, set aside and strain the mixture and discard the tea leaves. Pour the mixture back in the pot and stir in salt, sugar and the set-aside lemon peel and rosemary. Stir until salt and sugar are dissolved. Stir in the ice, cool to below 50 degrees F. Line a large pot with two 30-gallon plastic garbage bags, one inside the other. Place turkey in the bag-lined pot, breast-side down. Pour brine over turkey; press to submerge. Twist off bags to eliminate air pockets and tie. Refrigerate turkey in brine for 2 days (48 hours).
Drain turkey, discard brine. Pat turkey dry. Stuff cavity with rosemary, punctured lemons, celery and onion. Fold wing tips under; tie legs. Rub olive oil all over the turkey.
Place oven rack in the lowest third of the oven and preheat to 350 degrees F. Place turkey on a rack in large roasting pan. Place bird in oven and roast for 2 hours, then baste with 1/2 cup broth.
Continue to roast until turkey is brown and thermometer inserted into the thickest part of the thigh registers 165 degrees F. Basting frequently with the remaining 1 1/2 cups broth and pan juices. Cover loosely with foil if browning too quickly. Transfer turkey to a large platter or carving board. Tent loosely with foil. Let stand at least 30 minutes or up to 45 minutes prior to carving.