Preheat the oven to 425 degrees Fahrenheit.

Roll out the pie dough to line a 10-inch pie plate.

In a medium saucepan, melt the butter over medium heat. Add the flour and stir thoroughly to form a paste. Add the sugars and lemon juice and cook, stirring frequently, until bubbly and thick. Remove from heat.

Put the sliced apples in a medium-sized bowl. Pour the melted butter and sugar mixture over the apples and stir to coat the apples. Pour the apples into the pastry lined pie plate, then use the remaining pie dough to make a lattice crust.

Bake the pie for 15 minutes, then reduce the heat to 350 degrees and bake for a further 35-45 minutes until the crust is golden brown and the pie filling is bubbly. Remove from oven and let cool.