In a medium saucepan, whisk together sugar, cornstarch, and salt. Gradually stir in water until smooth.
Cook over medium heat, stirring constantly, until mixture thickens and boils. Boil for 1 minute, then remove from heat.
Gradually whisk about 1/2 cup of the hot mixture into the beaten egg yolks, then return all to the saucepan. Cook for 2 more minutes, stirring constantly.
Remove from heat and stir in butter, lemon juice, and lemon zest until smooth.
Pour filling into the pre-baked pie crust. Top with whipped cream or meringue if desired.
Bake for 10-12 minutes if using meringue, or chill for at least 2 hours if using whipped cream.