In a medium mixing bowl stir together 2 cups flour and salt. Using a pastry blender, cut in shortening until pieces are pea-size. Sprinkle 1 tablespoon of the water over part of the mixture; gently toss with a fork. Push moistened dough to side of bowl. Repeat, using 1 tablespoon water at a time, until all dough is moistened. Divide in half. Form each half into a ball.
Preheat oven to 375 degree F. In a large mixing bowl combine granulated sugar and flour. Add cranberries and lemon slices. Gently toss to coat.
Transfer fruit mixture to pastry-lined pie plate. For lattice top, roll remaining pastry into a 12-inch circle. Cut pastry into 1/2-inch-wide strips. Fill pastry-lined pie plate with filling. Weave strips over filling. Press the ends of pastry strips into crust rim. Fold the top pastry over the bottom pastry strips. Use the tines of a fork to seal the edge.
Trim pastry to edge of pie plate. Press the tines of a fork lightly into pastry around entire edge of pie.
Combine egg white and water; brush onto pastry. Sprinkle with coarse sugar.
To prevent overbrowning, cover the edge of the pie with foil. Bake for 25 minutes. Remove foil. Bake for 30 to 35 minutes more or until top is golden brown and filing is bubbly. Cool on a wire rack. Makes 8 servings.