Preheat oven to 425 degrees fahrenheit.
Peel, core, and slice apples thin. Place them in a large bowl, sprinkle the cinnamon onto the apples and stir to combine thoroughly.
To make the caramel sauce, in a medium saucepan, melt butter then whisk in flour until combined. Add brown sugar, granulated sugar and water and mix to combine well. Bring to a boil then lower heat and allow to simmer for 3 minutes. Stir in lemon juice.
Pour caramel sauce over prepared apples and stir well to thoroughly incorporate and coat each apple. The sauce will thin out as you stir from the juices of the apples, so make sure to really combine and cover all of the apples.
Place your bottom pie crust into your pan and gently spoon the apple pie filling into the pie crust and smooth to even out. Place the top crust on and trim any excess crust. Pinch the crust to seal the top and bottom edges. Cut slits into the center of the crust to allow steam to escape. Brush crust with milk. Use aluminum foil or a pie shield to cover the edges of the pie.
Place your pie on the center rack and bake for 50 minutes or until the crust is golden. Allow the pie to cool for at least a full hour before cutting. This pie is actually best served the following day.