In a medium saucepan, combine the sugar and cornstarch. Stir in the water, blending until smooth. Cook over medium heat until the mixture boils, stirring constantly. Boil 1 minute. Remove from heat.
Blend a small amount of the hot mixture into the beaten egg yolks. Return this to the saucepan, mixing well. Cook just until the mixture starts to boil, stirring constantly. Reduce the heat to medium low and continue stirring and cooking until the mixture is very thick. Remove from heat.
Stir in the butter, lemon peel, and juice.
Meanwhile, prepare the meringue. In a large mixing bowl, beat the egg whites, vanilla extract, and cream of tartar until small peaks form. Gradually beat in the sugar, 1 tablespoon at a time until stiff peaks form. The meringue should be stiff and glossy.
Pour the cooled filling into the prepared pie shell. Spoon the meringue over filling, sealing to edges of the crust and spreading to cover. Add some decorative swoops if you like.
Bake at 400 degrees until the meringue is golden brown, about five to 10 minutes. Remove the pie to a cooling rack. Cool the pie for several hours before serving.
Promptly store leftovers in an airtight container in the refrigerator, for up to 3 days.Nutritional values are approximate and based on ⅛ of the recipe. If you prefer, you can omit the meringue and serve the pie as a tart with whipped cream.