In a large bowl, mix sliced apples, lemon juice, both sugars, flour, cinnamon and nutmeg. Pile into crust.
Prepare topping: In a medium bowl, with a pastry blender or a fork, mix flour, both sugars, and butter until coarsely crumbled. Sprinkle evenly over apples.
Bake at 375°F for 50 minutes. (If your crust gets too brown early on, cover the edges of the pie crust with tin foil and continue baking)