In the bowl of a food processor, combine the flour, sugar, and salt. Pulse briefly to blend. Add the cubed butter and shortening, then pulse several times until the mixture resembles coarse crumbs. Gradually add the ice water, pulsing just until the dough begins to come together. Avoid overmixing. Divide the dough into two equal portions, shape into discs, wrap each in plastic wrap, and refrigerate for a minimum of 30 minutes.

Preheat the oven to 400°F (200°C). Prepare a 10x15-inch jelly roll pan or rimmed baking sheet by lightly greasing or lining it with parchment paper.

In a large mixing bowl, combine the strawberries with the sugar, cornstarch, lemon zest, and 2 tablespoons of lemon juice. Stir gently to coat the strawberries evenly. Set the mixture aside for 10–15 minutes to allow the sugar to draw out the fruit's juices.

On a lightly floured surface, roll out one disc of chilled dough into a rectangle approximately 12x17 inches. Carefully transfer it to the prepared pan, gently pressing the dough into the corners and up the sides. Trim any excess dough if necessary.

Pour the strawberry filling into the crust-lined pan, spreading it evenly. Lightly brush the edges of the dough with the beaten egg to help seal the top crust.

Roll out the second disc of dough into a rectangle large enough to cover the pie. Either create a lattice using strips of dough or place the full sheet over the filling and cut several small slits to allow steam to escape. Press and crimp the edges to seal, then brush the surface of the crust with the remaining egg wash.

Bake in the preheated oven for 45 to 50 minutes, or until the crust is golden brown and the filling is visibly bubbling through the vents. If necessary, tent the edges with foil during the last 10–15 minutes to prevent over-browning.

Remove the pie from the oven and allow it to cool on a wire rack for at least 1 hour before slicing and serving. This will help the filling set properly.