Lightly spoon 2 1/2 cups flour into dry measuring cups; level with a knife. Combine 2 1/2 cups flour and salt in a large bowl; cut in 6 tablespoons butter and vegetable shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add lemon juice. Sprinkle surface with ice water, 1 tablespoon at a time, and toss with a fork until moist and crumbly. Shape dough into a ball, and wrap in plastic wrap. Chill 1 hour.
Divide dough into 2 equal portions. Gently press each portion into a 1-inch-thick circle on heavy-duty plastic wrap; cover and freeze 10 minutes.
Preheat oven to 350°.
Place apples in a large bowl. Combine sugar, 1/4 cup flour, cinnamon, and allspice in a small bowl. Sprinkle sugar mixture over apples; toss well to coat.
Working with 1 dough portion at a time, roll dough into a 12-inch circle on a lightly floured surface. Fit dough circle into a 9-inch pie plate coated with cooking spray, allowing dough to extend over the edge. Roll the remaining dough portion into a 10-inch circle on a lightly floured surface. Spoon apple mixture into prepared pie plate, and dot with 1 tablespoon butter. Drizzle apple mixture with 1/2 teaspoon vanilla. Top with 10-inch dough circle. Press edges of dough together. Fold edges under, and flute. Brush surface of dough with milk. Cut 3 (1-inch) slits in the top of dough to allow steam to escape. Bake at 350° for 1 hour or until the apples are tender.