Put the lemon juice, 2/3 cup water and lemon zest in a medium saucepan. Bring to a boil over medium-high heat. Once boiling, slide the pan off the heat, cover and set aside for 15 to 20 minutes to steep.
Put the 1 cup sugar, cornstarch, pinch of salt and cayenne in a medium bowl and whisk until blended. Pour the juice mixture through a fine-mesh strainer over the bowl, pressing on the solids to release all the juices; discard the solids.
Add the heavy cream and yolks, and whisk until blended. Pour and scrape the mixture back into the saucepan. Cook, whisking constantly, over medium heat until it comes to a full boil. Boil, whisking constantly, for 45 seconds.
Pour and scrape the filling into the pre-baked pie crust, smooth and cover the surface directly with plastic wrap. Refrigerate until well-chilled and very firm, about 6 hours.
To finish the pie, position a rack in the center of the oven and preheat to 375 degrees.