Make crust. In a food processor, pulse flour, sugar and salt to blend. Add cubed butter and lard and pulse on/off until mixture resembles coarse meal. You should still see pieces of butter and lard. Transfer mixture to bowl and add 5 tablespoons of ice water. Mix with a fork until dough starts to clump together. If too dry, add more ice water by teaspoonfuls until you can gather dough into ball. Divide in half and flatten each half into a disc. Wrap tightly in plastic wrap and refrigerate for AT LEAST 1 hour.
Preheat oven to 425º. About 15 minutes or so before dough is ready to roll, make filling. In bowl, combine sliced peaches, sugar, tapioca and lemon juice. Set aside and let sit for 15 minutes.
In small dish, whisk together egg and milk, set aside.
Remove 1 disc of dough. Lightly flour work surface and rolling pin. Roll dough from center out, turning frequently and adding more flour if sticking. Transfer dough to glass pie dish and gently press into place. Trim excess dough but leave some overhang. Patch any holes or tears with dough scraps. Return to refrigerator while you roll the 2nd disc for the top.
As with the bottom, roll the top disc into a large round to top the pie. Remove bottom crust in the plate from refrigerator. Fill with peach mixture and then dot with 1 tablespoon butter.
Carefully place top crust over filling. If you can, try rolling the dough around the pin and then unroll it over the filling. Trim excess dough and roll under edges and crimp, with a fork or flute with thumb and index finger. Brush top and edges with egg wash and sprinkle with sugar. Using a small knife, cut 4 or 5 slits in top crust to vent.
Place pie on baking sheet and bake in middle of oven for 20 minutes. Turn heat down to 375º and continue baking until crust is browned and juices are bubbling, about 30-35 minutes. Cool completely before cutting.