**Prepare the Pie Crust**
Preheat your oven to 350°F (175°C). If using a store-bought pie crust, bake it according to package instructions until golden and crisp. If making homemade crust, roll out the dough on a floured surface and fit it into a 9-inch pie dish. Prick the bottom with a fork and bake for 10-12 minutes, or until golden. Let the crust cool while you prepare the filling and meringue.
**Make the Lemon Filling**
In a medium saucepan, whisk together the granulated sugar, cornstarch, and salt. Add the water and whisk until smooth. Cook over medium heat, stirring constantly, until the mixture begins to thicken and comes to a gentle boil.
In a separate bowl, whisk the egg yolks until smooth. Slowly add about 1/2 cup of the hot sugar mixture into the egg yolks, whisking constantly to temper the eggs. Gradually pour the egg yolk mixture back into the saucepan with the remaining sugar mixture, whisking continuously.
Cook for an additional 2-3 minutes until the filling is thick and glossy. Remove from heat and stir in the fresh lemon juice, lemon zest, and butter until fully incorporated.
**Prepare the Meringue**
In a mixing bowl, beat the egg whites with the cream of tartar using an electric mixer on medium-high speed until soft peaks form. Gradually add the granulated sugar, 1 tablespoon at a time, continuing to beat until stiff, glossy peaks form. Add the vanilla extract and beat for another 30 seconds.
**Assemble the Pie**
Pour the lemon filling into the pre-baked pie crust, spreading it evenly. Spoon the meringue over the lemon filling, spreading it to the edges of the crust to seal in the filling. Use a spatula to create peaks in the meringue.
**Bake the Pie**
Bake the pie in the preheated oven at 350°F (175°C) for 10-12 minutes, or until the meringue is golden brown. If the meringue begins to brown too quickly, you can cover the edges of the crust with aluminum foil to prevent overbaking.
**Cool and Serve**
Allow the pie to cool at room temperature for at least 2 hours to allow the filling to set. After cooling, slice and serve. The pie can be stored in the refrigerator for up to 3 days.