Preheat the oven to  325 degrees F (162 degrees C).

To make the filling: Whisk 1 cup sugar, flour, cornstarch, and salt together in a medium saucepan; stir in water, lemon juice, and lemon zest. Cook over medium-high heat, stirring frequently, until mixture comes to a boil. Stir in butter.

Place egg yolks in a small bowl and gradually whisk in 1/2 cup of hot sugar mixture. Whisk egg yolk mixture back into remaining sugar mixture. Bring to a boil and continue to cook while stirring constantly until thick. Remove from heat; pour filling into baked pastry shell.

To make the meringue: Beat egg whites in a glass, metal, or ceramic bowl until foamy. Gradually add sugar, continuing to beat until stiff peaks form. Spread meringue over pie filling, sealing the edges at the crust.

Bake in preheated oven until meringue is golden brown, about 20 to 25 minutes.