Stir together sugar, flour, cinnamon, nutmeg, allspice and salt. Set aside
Peel and slice apples. Stir lemon juice and zest with the apples. Then add dry ingredients to coat the apples. Then add dry ingredients to coat the apples. Arrange the fruit into the pastry lined pie dish.
Melt the butter for the topping. Stir in the brown sugar, flour and cornmeal. Pat the crumb mixture in place, covering the surface of the apples.
Bake the pie at 425°F for 20 minutes. Reduce the heat to 350°F and bake for another 25 minutes. Let cool before serving.