One day before: Combine maple syrup, sugar, soy sauce, lemon juice/quarters, salt, garlic, bay leaves, and peppercorns in a 6-quart pot. Add water and simmer until sugar and salt dissolve. Cool completely. Place turkey in a container large enough to fit the whole bird. Pour cooled brine over turkey, making sure it is submerged. Refrigerate for at least 8 hours or up to 18 hours. After brining, remove turkey from brine, rinse well, and pat dry. Discard the brine. Place turkey, breast side up, in a roasting pan. Place, uncovered, in the refrigerator overnight so the skin dries for better browning.
Start gravy:
One day before: Heat 2 tablespoons butter and the oil in a 12-inch skillet over medium heat. Add shallot and cook, stirring, until just soft, 1-2 minutes. Add stock and sherry and cook over high heat until reduced to about 3 cups, about 15 minutes; it will be thickened later. Refrigerate until day of serving.
Roast turkey and finish gravy:
Day of serving: Remove turkey from the refrigerator at least 1 hour before cooking to bring to room temperature. Position oven rack in lower third of oven, and preheat the oven to 400°F.
Mix softened butter with salt, pepper, and garlic powder. Gently loosen skin away from breast meat and rub half of the softened butter mixture all over the breast, under the skin, while taking great care not to tear it. Rub remaining half of butter over outside of the bird, on breast and legs.
Stuff onions and lemons into the cavity. Tuck wings under and tie legs together with kitchen twine.
Roast the turkey for 30 minutes. Lower temperature to 350°F and pour 1 cup of broth into the bottom of the pan. Cook for about 2 more hours (depending on oven and size of bird). Baste turkey every 30 minutes, checking to ensure the turkey doesn’t brown too much.
Roast until skin is golden brown and an instant-read thermometer registers 160°F in thickest area of thigh, about 2½ hours total cooking time (begin checking earlier if bird is smaller). If skin is overbrowning, cover breast loosely with foil.
Note: A brined turkey will cook faster than an un-brined one, so watch turkey carefully.
Transfer to a cutting board, tent with foil, and let rest 30 minutes. Pour pan drippings into fat separator and allow fat to rise to top.
Just before serving, bring previously prepared gravy to a simmer over medium-low heat. Mix cornstarch with 3 tablespoons water. Stir mixture into gravy, a little at a time, until thickened to your liking (you may not need it all). Whisk in separated pan drippings and remaining 2 tablespoons butter and chives. Season to taste with salt and pepper.