For the turkey and brine: In a large pot on medium-high heat, add 6 quarts (1 1/2 gallons) water, the salt, peppercorns, lemon, sage and thyme. Bring to a boil, lower to a simmer and cook until the salt is dissolved and the water is fragrant. Let cool.
Put the turkey in a roasting bag, large plastic bag or a 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 in with the turkey for brining. Refrigerate for at least 8 hours and up to 3 days.
When ready to cook, remove from the refrigerator and discard all of the brining liquid and solids. Pat the turkey dry with paper towels. Place the turkey breast-side up on a wire rack resting in a roasting pan/baking dish and allow to sit on the countertop for about 2 hours to come to room temperature.
For roasting: Preheat the oven to 400 degrees F.
Using your finger, gently release the skin from the muscle of the turkey and insert the butter pieces between the layers all over the bird. Season the skin with salt and pepper. Put the roasting pan in the oven, pour the beer into the bottom of it and lower the heat to 350 degrees F. Roast, basting every 30 minutes, until an instant-read thermometer inserted in the thigh reads 160 degrees F, 3 to 3 1/2 hours. Let rest for 30 to 45 minutes before glazing and slicing.
For the glaze: In a large nonstick pan on medium heat, add the pecans and cook, tossing, until fragrant, about 4 minutes. Remove the pecans to a plate and add the butter, paprika, pumpkin pie spice and sage to the same pan. Once the butter is melted and the pan is fragrant with sage, remove the sage and add the honey and pecans to the pan. Raise the heat until the mixture begins to simmer, then remove from the heat. Pour over the rested turkey, slice and serve.