PREHEAT oven to 425 degrees F. MELT the butter in a saucepan. STIR in flour to thicken. ADD water, white sugar, brown sugar, cinnamon, nutmeg, vanilla and lemon juice and bring to a BOIL. REDUCE temperature and let SIMMER.
PLACE the bottom crust in your pan. BRUSH with an egg white to prevent crust from getting soggy.
MIX the syrup with the apples. FILL the bottom crust with apples. COVER with top crust. CUT vents in the top crust for the steam to escape through. BRUSH the top crust with egg whites.
PLACE pie on the middle rack of the oven. BAKE 15 minutes in the preheated oven. REDUCE the temperature to 350 degrees F. Continue baking for 35 to 45 minutes, until apples are soft.