Heat immersion circulator to 160°F (71.1°C).
Place apples, cranberries and lemon juice in vacuum sealable bag. In a 1 cup measure with a spout, mix sugar, cornstarch, cinnamon and salt. Pour sugar mixture over fruit in bag; seal bag closed. Place apple scraps (peels and core) in another vacuum sealable bag; seal it closed. Submerge fruit and apple scrap bags in water bath and cook sous vide for 1 hour.
Remove both bags from immersion circulator. Open fruit bag and drain over a sieve reserving the juice in a small saucepan. Place fruit in large bowl. Cut a small slit in the scraps bag and squeeze out as much juice as you can into the saucepan. Discard scraps. Heat reserved juice, stirring, to a boil. The juice should become slightly thickened and clear. Pour juice over fruit; chill in the refrigerator until completely cold.
Blend flour and salt in a mixing bowl. Cut in lard and butter with a pastry blender until mixture forms pea-sized crumbs. With a fork, stir in just enough water until dough holds together. Divide dough into 2 disks, one slightly larger than the other, wrap and chill at least 30 minutes.
Heat oven to 425°F (218°C).
On lightly floured surface roll out larger disk of dough to fit a 9-inch pie dish; ease crust into pie dish. Pour chilled filling into crust. Roll out remaining crust and cover filling. Trim, seal and crimp edges. Brush crust lightly with egg white. Sprinkle with sugar. Cut slits in top of pie to allow steam to escape.
Bake pie for 20 minutes. Reduce oven temperature to 375°F (190°C) and bake 30 to 40 minutes or until filling bubbles and crust is golden brown. Cool.