Preheat oven to 350 °F
Make the filling by whisking 1 cup sugar, flour, cornstarch, and salt in a medium saucepan. Stir in water, lemon juice, and lemon zest. Cook over medium heat, stirring frequently, until mixture comes to a boil.
Put egg whites in a small bowl and gradually whisk in 1/2 cup of the hot sugar mixture. Next, whisk egg yolk mixture into the remaining sugar mixture. Bring to a boil and continue to cook, stirring constantly, until the mixture is thick. Remove from heat and pour into the baked pie crust.
Make the meringue by beating the egg whites in a metal mixing bowl until foamy. (Glass or ceramic bowls are an alternate.) Gradually add the sugar, continuing to beat until stiff peaks form. Spread the meringue over the pie filling, sealing the edges at the crust.
Place pie in the oven and bake until the meringue is golden brown. (Approximately 10 minutes.)