How to Make It
Preheat oven to 425°F. Unroll 1 piecrust, and fit into a 9-inch pie plate. Stir together strawberries, sugar, cornstarch, tapioca, lime zest, lime juice, and vanilla in a large bowl. Spoon mixture into prepared pie plate; top evenly with butter cubes.
Roll out remaining piecrust onto a lightly floured surface. Cut into 1 1/4-inch-wide strips; place on top of pie in a lattice pattern. Whisk together egg and water in a small bowl; brush lattice and edges of pie with egg mixture. Sprinkle evenly with demerara sugar. Place pie on a baking sheet lined with aluminum foil.
Bake in preheated oven until edges are golden brown, 15 to 20 minutes. Reduce oven temperature to 375°F; cover edges of pie with aluminum foil. Bake until pie is bubbling and crust is golden brown, 45 to 50 minutes. Transfer to a wire rack, and cool completely, about 3 hours.