Combine the sliced peaches and sugars in a bowl. Cover with clear plastic wrap and set aside for 45 minutes to one hour. Then, drain sugar-peaches and reserve syrup.
Meanwhile, line your baking dish with one sheet of pie dough.
Next, prepare the lattice crust top. Lightly sprinkle a flat surface with a small amount of flour and lay the second piece of dough on it. Using a pizza cutter, slice dough into strips but be careful not to slice your strips too thin, as they will shrink slightly during baking.
Add flour, cornstarch, cinnamon and nutmeg to a small saucepan. Pour peach syrup (from drained peaches) into a small saucepan. Slowly add syrup to the pan, stir and bring to a boil.Cook until just thickened, about 2–3 minutes. Remove from heat. Stir in lemon juice and butter.Preheat your oven to 400°.
Pour peach mixture into prepared pie crust dish.
Lay vertical pie crust strips across the top of the pie (leave gaps in between). Then, roll back every other pie strip—lay a horizontal strip across and lay vertical strips down. Rollback every other vertical pie strip (not the same ones you just rolled) back to the point of your new horizontal line, placing your next horizontal strip while leaving a gap between strips, and lay pulled back strip over top. Repeat again and again to create a basket weave effect.Crimp the strips into the edge of the bottom crust to join them. Loosely cover the edge of the pie crust with foil and cook in a 400° oven for approximately 45 minutes or until the crust is golden brown and the filling is nice and bubbly.Cool in the pan on a wire rack.