Make the dough. Mix 1 1/4 cups flour, 1 teaspoon sugar, and 1/2 teaspoon salt, cut in the butter and shortening until crumbly, then stir in the ice water until the dough holds together. Shape into a disk, wrap, and chill for 30 minutes.
Make the topping. Whisk the flour, brown sugar, cinnamon, and salt, then rub in the cold butter until large clumps form. Chill until needed.
Fill the crust. Heat the oven to 425 degrees F. Roll out the dough, fit it into a 9 inch dish, toss the apples with the sugar, flour, and lemon juice, and pile them in.
Add the crumbs. Sprinkle the topping evenly over the apples, pressing lightly so it stays in place.
Bake in two stages. Bake at 425 degrees F for 15 minutes, then lower to 350 degrees F and bake 30 to 35 minutes until the topping is golden and the filling bubbles. Tent with foil if it browns too fast.
Cool. Cool for at least 2 hours before slicing so the filling sets.