Preheat the oven to 400°F.

In a saucepan, combine 1 cup sugar, flour, cornstarch, and salt. Whisk in water and lemon juice. Cook over medium heat, stirring constantly, until thickened.

In a small bowl, slightly beat egg yolks. Gradually whisk in half a cup of the hot sugar mixture. Then, whisk the egg yolk mixture back into the remaining sugar mixture in the saucepan. Cook for 1 more minute, stirring constantly.

Remove from heat. Stir in butter and lemon zest. Pour into the pre-baked pie crust.

For the meringue, beat egg whites with cream of tartar until foamy. Gradually add 1/3 cup sugar, beating until stiff peaks form.

Spread meringue over pie filling, sealing the edges at the crust.

Bake in the preheated oven for about 5 minutes, or until meringue is golden brown.

Allow the pie to cool on a wire rack until completely cool. Refrigerate for 3-6 hours before serving.