In a medium-sized saucepan, whisk the cornstarch into the water and lemon juice completely. If desired, in the grated lemon zest as well.
Stir the sugar and salt into the mixture. Bring to a boil, stirring constantly and let boil for a minute. Remove from the heat and stir in the butter until melted.
Take the egg yolks and whisk them until they are light yellow. Save your egg whites for the meringue topping!
You now need to temper the eggs. Take a couple tablespoons of the hot liquid from the pot and whisk it rapidly into the egg yolks completely. Then you can whisk the yolks into the pot of hot liquid safely, without lumps forming. Whisk them in entirely, then cook for another 3-4 minutes until thickened. Remove from the heat.
Let the filling cool enough that it won't seep through the bottom crust badly, but not until it sets, then spoon into the baked pie shell.
In a large bowl, whip the egg whites and cream of tartar until foamy.
Add the sugar gradually and continue to whip until stiff peaks form. Beat in the vanilla.
Spread the meringue over the pie as you wish. I used an icing bag and a large tip to pipe some lovely stars onto the top of mine; meringue pipes so beautifully.
Preheat your oven to 325 degrees and bake your meringue until it's as golden as you like. I prefer mine very brown and you have to watch it very, very carefully to achieve this. Start checking at 5 minutes and you may have to rotate it in the oven to make sure the little peaks of meringue get browned evenly.
I like the extra zing of lemon zest, however it does make the filling have little zest pieces in it. If you want it completely smooth, leave out the zest.