Prepare a 9-inch pie plate.
Add the flour and salt to a large bowl.
Cut in the butter and shortening with a knife or with your hands until the mixture consists of marble-sized lumps.
Begin to add the ice water a few tablespoons at a time, continuing to toss the mixture together.
The dough is moist enough when you can squeeze a ball together in your hand.
Cut the dough in half. Roll each half into a ball and flatten into a disk.
Flour the counter and roll each disk out to about a 12-inch round.
Place one of the pastry rounds on the bottom of the pie plate.
Preheat the oven to 425°F.
Prepare the filling by adding the 4 beaten eggs, salt, and flour to the lemon and sugar mixture. Combine well but don’t beat.
Pour the lemon filling into the shell.
Top with the second pie crust and press around the edges. You can use fingers, a spoon or fork to make a pattern around the edge. Moisten with cold water if it begins to get sticky.
Brush the top of the pie with the remaining beaten egg.
Cut 2-4 vents in the top of the pie with a sharp knife.
Bake in the oven for about 20 minutes.
Reduce the oven temperature to 375°F.
Bake for another 25 minutes.
Allow the pie to cool before cutting into slices.