Put the water, kosher salt, brown sugar, half of the thyme, and the peppercorns in a large pot. Squeeze all but 3 of the lemon wedges and put the wedges into the pot. Bring to a boil just for a minute, stir so the kosher salt and brown sugar dissolves. Let this cool completely, add ice cubes if needed.

If the pot is large enough, put the turkey into the pot with the brine. Or transfer the brine to a larger container and add the turkey. Refrigerate 24 to 36 hours.

Remove the turkey and pat dry, discard the brine. Put the remaining lemon wedges and fresh thyme into the turkey cavity. Sprinkle lemon pepper seasoning on the turkey.

Place the turkey directly onto the smoker or Traeger pellet grill set between 225-250 degrees for about 30 minutes per pound, approximately 7 to 9 hours.

Or put the turkey in a roasting pan and place in a 325 degree oven for about 15 minutes per pound, approximately 3 1/2 to 4 1/2 hours.

Either cooking method, monitor the internal temperature and remove once it's at 160 to 165 degrees. Let it rest for 45 minutes before slicing.