In a medium saucepan, combine the granulated sugar, cornstarch, salt, and water. Whisk together until smooth. Place the saucepan over medium heat and bring to a gentle boil, stirring constantly. Once it starts to thicken (about 5 minutes), reduce heat to low.
In a separate bowl, whisk the egg yolks until smooth. Carefully add a few spoonfuls of the hot sugar mixture to the yolks to temper them, stirring continuously to prevent curdling. Once tempered, slowly add the yolk mixture back into the saucepan, continuing to stir.
Remove the saucepan from the heat and stir in the fresh lemon juice, grated lemon zest, and the butter pieces. Mix until the butter is fully melted and the filling is smooth. Set aside to cool slightly.
In a clean mixing bowl, beat the egg whites on medium speed until foamy. Add the cream of tartar and continue beating until soft peaks form. Gradually add the granulated sugar and beat until stiff peaks form. Finally, mix in the vanilla extract.
Pour the lemon filling into the prebaked pie crust, smoothing it out with a spatula. Immediately spread the meringue over the top, making sure to seal the edges to prevent shrinking. Use the back of a spoon to create peaks and swirls for a beautiful finish.
Preheat your oven to 350°F (175°C). Bake the pie for approximately 10-15 minutes, or until the meringue is lightly golden. Keep an eye on it to avoid over-browning.
Allow the pie to cool at room temperature for about an hour before transferring it to the refrigerator. The pie can be made a day in advance, making it a perfect make-ahead dessert!