"My husband helped me pick the apricots off the tree when we made this pie. We had the best time together because we knew there would be a delicious pie at the end. It takes us back to 1800's when people ate what they grew. This pie is not as sweet as you might think. It is tart with a good texture. Serve with vanilla ice cream."
Place apricots in a large bowl. Squeeze lemon halves over apricots. Gently mix 1 cup white sugar, brown sugar, flour, and 2 tablespoons cinnamon into apricots to coat.
Line a 9-inch pie dish with 1 pie pastry. Spread apricot filling into shell. Roll remaining pastry onto a work surface; cut into about 1/2-inch-wide strips for a lattice crust. Cover apricot filling with pie dough strips creating a lattice pattern; seal top crust pieces to bottom crust edges and crimp into a fluted pattern. Brush egg white over top crust and sprinkle with a pinch of white sugar and cinnamon. Cover fluted crust edges loosely with aluminum foil.
Bake in the preheated oven until filling is bubbling and crust is golden brown, 45 to 55 minutes. Remove pie from oven and cool.