In food processor, combine flour, shortening, lemon peel, and salt. Pulse to blend. Add butter; pulse for 3 seconds. Pour in the cold water; pulse 3 to 4 seconds more. Gather dough together, and divide into 2 balls; flatten into disks, wrap in plastic, and refrigerate 1 hour or up to 3 days.
Place a large piece of foil on the bottom oven rack to catch drips. Heat oven to 400°F. Roll 1 pie-dough disk into a 12-inch circle, then place in a 9-inch pie pan. Refrigerate until ready to fill.
In a large bowl, combine berries, 1 cup sugar, and tapioca. Roll remaining pie-dough disk into a 10-inch circle; cut into 3/4-inch-wide strips using a pasta wheel or pizza cutter.
Fill pie shell with berry mixture; cover top with strips of dough, weaving to make a lattice pattern. Pinch top and bottom crusts together to seal. In small bowl, whisk egg white with 1 tablespoon water, then brush over top crust. Sprinkle with remaining 1 tablespoon sugar.
Bake on top oven rack for 20 minutes, then reduce oven temperature to 375°F. Bake 1 hour more, or until crust is browned and pie is bubbling. Let cool on wire rack.