For the brine: Combine the sage, thyme, lemon, salt, peppercorns and 1 1/2 gallons water in a large pot over medium-high heat. Bring to a boil, then lower the heat to a simmer and cook until the salt is dissolved and the water is fragrant. Turn off the heat and let cool completely.
Place the turkey in a roasting bag, large plastic bag or bowl large enough to fit it with still more space to give. Pour in the brining liquid and seal or cover. If there's not enough room for all of the liquid in the brine, be sure to at least include the herbs, lemon and peppercorns. Refrigerate at least overnight or up to 3 days. When ready to cook, remove from the refrigerator and discard all of the brining liquid and solids.
For the turkey: Pat the turkey dry with paper towels. Place the turkey cavity-side down on a wire rack resting in a roasting/baking dish and allow to sit on the countertop for about 2 hours to come to room temperature.
Using kitchen shears or a knife, cut the backbone of the turkey out and break the breastbone to open up and flatten the bird by gently pressing down with the skin-side up. Flip over and pat dry. Using your finger, gently release the skin from the muscle of the turkey and insert the butter pieces between the skin and meat all over the bird. Drizzle with olive oil and sprinkle the skin with salt and pepper.
Preheat the grill to 400 degrees F.
Place the turkey over direct heat skin-side down. Lower the heat to 350 degrees F and close the lid of the grill. Cook until the turkey releases from the grates and reveals grill marks, about 20 minutes.
Meanwhile, make the glaze: Heat the olive oil and black pepper together in a large nonstick pan over medium heat. Steep over medium heat until the oil smells and tastes like pepper, 6 to 8 minutes. Add the honey, Worcestershire sauce, lemon zest and lemon juice to the same pan. Raise the heat to medium-high and cook, stirring occasionally, until the mixture begins to simmer and slightly reduce. Remove from the heat and rest until it tightens a bit, about 2 minutes.
Flip the turkey and glaze the skin with the lemon pepper glaze. Close the lid of the grill and continue to cook, glazing every 30 minutes, until an internal-read thermometer inserted in the thigh reads 160 degrees F, 1 to 2 hours. Remove the turkey form the grill and let rest at room temperature tented with aluminum foil for 30 minutes before carving.