Special equipment: a countertop indoor turkey fryer and an instant-read thermometer
In a saucepan, add the turkey stock, turkey neck, gizzards, thyme, bay leaf and shallot. Bring to a boil, reduce to a simmer and simmer for 30 minutes. Strain out the solids. If a chunky gravy is desired, chop the gizzards and return them to the simmered stock in the saucepan. Keep warm.
In a straight-sided saute pan, add the hot oil and flour and cook over medium-high to high heat until the mixture is light brown in color (for a dark gravy, cook the flour to a deeper brown color). Add 2 cups of the warm stock, whisking constantly, and cook until the gravy thickens and bubbles. Add more warm stock if a thinner consistency is desired. Reduce the heat to low and add salt and pepper to taste (this will depend on how salty the stock is). Add a squeeze of lemon juice and taste again for seasoning. Keep warm until ready to serve, adding more warm stock as needed.
Just before serving, remove from the heat and swirl in the butter until melted. Pour into a gravy boat and serve.
Let the turkey come to room temperature, then pat it dry thoroughly and season it generously with salt and pepper inside and out.
Fill a countertop indoor turkey fryer with the indicated amount of oil according to the manufacturer's instructions (see Cook's Note) and heat to 400 degrees F. Carefully lower the turkey into the fryer and cook for 35 to 45 minutes. An instant-read thermometer inserted into the thigh should register approximately 165 degrees F. Transfer the turkey to a cutting board and let rest 30 minutes before carving.
If not making Deep-Fried Turkey, substitute 3 tablespoons neutral oil for the hot oil and heat in the saute pan for about 1 minute before adding the flour. To measure the amount of oil needed to fry the turkey, put the turkey in the fryer, add water to top of turkey and mark the water line with a crayon or marker. Remove the turkey and the water line will indicate how much oil will be needed to fry your turkey. Having too much oil can cause a fire. The pot should not be more than 3/4 full or the oil could overflow when the turkey is added. Dry the fryer before adding the oil.