Preheat the oven to 375°F. Place the prepared pie plate on a baking tray. In a medium-large bowl, toss together the apples and lemon juice. Add the sugar, flour, cornstarch, cinnamon, nutmeg, and allspice, and mix gently until the fruit is evenly coated. Stir in the apple cider, then transfer the filling to the prepared pie crust.
Cover the filling with the second crust. Cut five or six slits in the center of the dough, or cut out small shapes using a decorative cutter. This will allow steam to escape. Crimp the edges together by hand or with a fork to seal. (Alternatively, make a lattice crust: using a pastry wheel, cut long strips of dough from the remaining pie crust, then arrange in a lattice pattern. Trim the edges of the dough with scissors, then crimp the two crusts together to seal.) Brush the crust with a light, even coat of non-dairy milk, and sprinkle with the optional turbinado sugar for a sweet and sparkly finish.
Transfer the pie to the oven using the baking tray, and bake for 45 to 55 minutes, until the crust is golden-brown and the filling is thickened and bubbling. Remove from the oven, allow to cool on a wire rack, then serve.