Mix sugar, salt and corn starch in a saucepan. Whisk in water and beaten egg yolks. Cook over medium heat, stirring with a whisk constantly until mixture reaches a boil. Reduce heat and continue stirring for 1 minute until very thick. Be careful not to let the mixture scorch on the bottom of the pan.
Remove from heat; stir in lemon juice, lemon zest and butter until smooth.
Pour the hot filling into pie crust.*
Meringue
Fill a medium pot with about 1-inch of water, and bring it to a simmer over low heat. In a heatproof bowl that fits snugly on top of the pot without touching the water, whisk together the egg whites, sugar and salt.
Place the bowl with the egg white mixture over the saucepan of simmering water, creating a double boiler. Make sure the bottom of the bowl does not touch the water.
Whisk the egg white mixture for 3-4 minutes over the simmering water, stirring constantly, until the sugar has completely dissolved. Test this by rubbing a small amount of the mixture between your fingers to check for any sugar granules.
Once the sugar has dissolved, remove the bowl from the double boiler, and wipe the bottom of the bowl to remove any moisture. This is important to prevent any water from getting into the meringue, as it can affect the texture.
Using a hand mixer or a stand mixer fitted with a whisk attachment, beat the egg white mixture on medium-high speed for 5-7 minutes until stiff peaks form. The meringue should be glossy and hold its shape when the beaters are lifted.
Spoon meringue over hot lemon filling, sealing meringue to the edges of the crust. Use the back of a spoon to swirl meringue and draw up into peaks.
Place your oven rack in bottom third of the oven.
Bake the pie for 10 minutes, until peaks are lightly browned. Cool at room temperature for 30 minutes.
Chill in the refrigerator for a minimum of 3 hours before serving.
Lemon meringue pie is best eaten within a day or two of being made, because as it sits, the meringue will start to weep and separate from the filling.
Notes
*Have all of your ingredients for the meringue weighed out and your double boiler set up with the water simmering before you start making your filling. This way as soon as your filling is done, you can put the egg whites and sugar on the double boiler to make the meringue. Putting your meringue on top of the filling while it is still hot helps to ensure a better seal. This buys you more time before your meringue will weep and separate from the filling in the fridge.