In a medium saucepan, whisk together the cornstarch, flour, and a pinch of salt until any lumps are broken up.
Add the water and sugar to the dry mixture and stir to combine. Place on the stove over medium-low heat, stirring constantly. You want to bring this to a low boil — be patient, it takes a while. You'll notice it gradually getting thicker as the cornstarch and flour do their work.
While the filling heats, lightly beat your 5 egg yolks in a separate bowl and set them nearby.
Once the mixture reaches a low boil and has thickened, remove it from the heat. Now we need to temper the egg yolks so they don't scramble. Slowly pour about a cup of the hot mixture into the beaten egg yolks, whisking constantly as you pour. This brings the eggs up to temperature gradually.
Pour the tempered egg mixture back into the saucepan with the rest of the filling. Return to the stove on low heat and cook for exactly 3 minutes, stirring constantly.
Remove from heat. Stir in the lemon juice and lemon zest. Then add the butter one tablespoon at a time, stirring until each piece melts before adding the next. The filling should look like a smooth, thick pudding.
Pour the filling into your baked pie crust and set aside while you make the meringue.