Combine flour and 3/4 teaspoon salt in a medium bowl; cut in shortening with a pastry blender until mixture resembles coarse meal. Sprinkle water over surface of flour mixture; stir with a fork until dry ingredients are moistened. Shape dough into a ball; chill.
Sauté onion, celery, and garlic in butter in a large skillet until tender. Combine cornstarch and chicken broth; stir until well blended. Add chicken broth mixture and whipping cream to sautéed vegetables, mixing well. Stir in crayfish tails, remaining salt, and pepper; set aside.
Roll half of pastry to 1/8-inch thickness on a lightly floured surface; fit into a 9-inch pie plate. Spoon crayfish filling into pastry shell.
Roll remaining pastry to 1/8- inch thickness; cut into 3/4-inchwide strips, and arrange in a lattice fashion over filling. Trim bottom pastry, and arrange lattice pastry in a decorative design on edges.
Bake at 350° for 45 minutes or until crust is golden brown.