In a medium saucepan, combine the cornstarch, flour, sugar, and warm water.
Gently whisk together over medium heat, until the mixture begins to boil and becomes slightly translucent. This will take about 3-5 minutes.
In a small bowl, whisk the egg yolks.
Pour the egg yolks into the saucepan, stirring constantly over medium heat, for about 30 seconds to one minute.
Remove from the heat, add in the lemon juice, butter, and lemon zest.
Slowly stir into the mixture. Once the mixture is well combined, and the butter has thoroughly melted into the mixture, pour into the baked pie crust. Set aside while the filling cools.
Preheat the oven to 350 degrees F.
Meanwhile, in a stand mixer fitted with the whisk attachment, whisk the egg whites for about 15-20 seconds or until soft peaks form, then slowly begin adding the ⅓ cup of sugar to the mixing bowl.
Continue mixing on medium to high speed, until the egg whites thicken and form stiff peaks.
Gently spoon the egg white mixture over the filling, covering the entire top of the pie. Be sure to completely cover, touching the crust.
Bake for 10-13 minutes, until the meringue begins to turn golden brown.
Remove from the oven and let cool to room temperature, then refrigerate for 3-4 hours until set. Slice and serve.