Preheat your oven to 425°F (220°C).
In a mixing bowl, combine the gluten-free flour and cold butter. Use a pastry cutter or your hands to mix until the mixture resembles coarse crumbs.
Add the ice water, one tablespoon at a time, until the dough comes together. Divide the dough in half, wrap in plastic, and refrigerate for at least 30 minutes.
In another bowl, combine the sliced apples, sugar, gluten-free flour, cinnamon, nutmeg, and lemon juice. Toss to coat the apples evenly.
Roll out one half of the dough on a floured surface and fit it into a pie dish. Add the apple filling.
Roll out the second half of the dough and place it over the filling. Trim and crimp the edges to seal. Cut a few slits in the top crust to allow steam to escape.
Bake for 50 minutes, or until the crust is golden brown and the filling is bubbly. Let cool before serving.