Unfold the pie crust and place in a 9-inch pie plate, pressing the crust firmly into the plate, then flute if desired. Bake the pie shell according to the package directions; let cool.
Meanwhile, in a medium saucepan, combine 1 cup sugar, the cornstarch, and salt; mix well. Gradually whisk in the water and milk, stirring until the cornstarch is dissolved. Cook over medium heat, whisking until the mixture comes to a boil.
In a medium bowl, lightly beat the egg yolks. Gradually whisk in about 1/2 cup of the milk mixture, then whisk the yolk mixture back into the saucepan. Simmer over low heat for 2 to 3 minutes,whisking occasionally.
Remove the pan from the heat and whisk in the butter and lemon juice. Pour the filling into the pie shell; set aside.
Preheat the oven to 350. In a medium bowl, with an electric beater, beat the egg whites with the cream of tartar until soft peaks form. Add the remaining 1/2 cup sugar and continue beating until stiff peaks form, making meringue.
Spread the meringue over the pie filling, sealing to the edges of the crust. Using a spatula or the back of a tablespoon, form peaks in the meringue, and bake for 12 to 15 minutes, or until the meringue is golden. Let cool, then slice and serve.