In a medium saucepan, combine 1 cup of sugar, cornstarch, and salt. Gradually stir in the water, blending until smooth.
Cook over medium heat, stirring frequently, until the mixture comes to a boil. Boil for 1 minute, then remove from heat.
Gradually whisk about half of the hot mixture into the beaten egg yolks, then return the yolk mixture to the saucepan, stirring constantly.
Bring back to a gentle boil and cook for an additional minute, or until the mixture has thickened.
Remove from the heat and stir in the lemon juice, zest, and butter until well combined. Let this lemon filling cool until it’s just warm.
Preheat your oven to 325°F (163°C).
In a large, clean mixing bowl, beat egg whites and cream of tartar until soft peaks form. Gradually add 1/2 cup of sugar and continue beating until stiff peaks form.
Gently fold the beaten egg whites into the lemon filling to lighten it. Then pour the mixture into the baked pie crust.
Bake for 25 to 30 minutes, or until the center is set and the top is lightly golden.
Remove the pie from the oven and let it cool on a wire rack.
Chill in the refrigerator for at least 4 hours before serving.