1. Preheat oven to 425°. Whisk together first 3 ingredients in a medium bowl. Cut shortening into flour mixture with a pastry blender or fork until mixture is slightly crumbly. Add milk, stirring with a fork until dry ingredients are moistened and mixture is soft enough to form a soft ball.
2. Turn dough out onto a lightly floured surface, and knead 6 to 8 times. Divide dough in half. Roll 1 dough half to 1/4-inch thickness on a lightly floured surface, and cut into 1-inch-wide strips. Place on a lightly greased baking sheet.
3. Bake strips at 425° for 15 minutes or until lightly browned. Transfer strips to a wire rack, and let cool completely (about 30 minutes). Reduce oven temperature to 350°.
4. Meanwhile, roll remaining dough half to 1/4-inch thickness; cut dough into 1-inch-wide strips.
5. Sprinkle 2 cups sugar, 1/3 cup flour, and lemon juice over fresh blackberries in a large bowl, and gently stir; let stand 10 minutes.
6. Spoon half of blackberry mixture into a lightly greased 13- x 9-inch baking dish. Break each baked dough strip into 2 or 3 pieces, and place on top of blackberry mixture in baking dish. Dot blackberry mixture with half of butter pieces. Spoon remaining blackberry mixture over baked dough strips.
7. Arrange unbaked dough strips in a lattice design over filling, and sprinkle with 1 Tbsp. sugar. Dot blackberry mixture with remaining butter pieces.
8. Bake at 350° for 50 to 60 minutes or until pastry is golden and mixture is bubbly. Serve with vanilla ice cream.