Build the brine: In a large pot, squeeze the lemon halves and drop them in along with the ginger, salt, sugar, thyme, onion quarters, peppercorns and 8 cups of water. Bring to a boil while stirring to dissolve the sugar and salt then lower to a simmer until the ginger is tender and the pot is fragrant, about 15-20 minutes. Remove from the heat and pour in the remaining 4 cups of ice water. Pour into a brining bag and allow to cool slightly.
Remove the neck bone and gizzards from the turkey, refrigerate both to use for gravy or rice. Add the turkey to the brining bag and press all of the air out then seal. Refrigerate 24 hours (not just overnight).