Preheat oven to 350°F (175°C).
In a medium saucepan, whisk together sugar, cornstarch, and salt. Gradually stir in water and lemon juice.
Cook over medium heat, stirring constantly until mixture thickens and comes to a boil. Boil for 1 minute, then remove from heat.
In a small bowl, beat egg yolks. Slowly whisk in a small amount of hot lemon mixture to temper, then return all to the saucepan.
Cook over medium heat for 2 more minutes, stirring constantly. Remove from heat and stir in lemon zest and butter until smooth.
Pour hot filling into the pre-baked pie crust.
In a clean bowl, beat egg whites and cream of tartar until soft peaks form. Gradually add sugar and beat until stiff, glossy peaks form.
Spread meringue over hot filling, sealing the edges at the crust.
Bake for 15–20 minutes, or until meringue is golden brown.
Cool at room temperature for 1 hour, then refrigerate for at least 3 hours before serving.