Cut two 8x16" pieces of parchment paper. Put the strips in a straight sided 8" square baking pan so that they cross each other and the excess hangs over the pan's sides. Push the parchment paper into the bottom and corners of the pan.
Position rack in the center of the oven and heat oven to 325 degrees. Break graham crackers into a food processor and process until finely ground. Add the melted butter and pulse until the mixture looks like damp sand. Transfer crumbs to the lined pan and press finrmly and evenly into the pan. Set aside.
Rinse, dry, and reassemble the food processor. In the bowl, combine cream cheese, sugar, lemon juice, and lemon zest. Process until smooth, about 30 seconds, stopping halfway to scrape the sides of the bowl. Add the eggs and process until the mixture is perfectly smooth and blended, stopping to scrape the sides of the bowl as necessary, about another 20 seconds. Pour the cheesecake mixture into the prepared pan. Bake until the sides are slightly puffed and the center is dry to touch, about 40 minutes,.
Make curd while the cheesecake bakes as it pours and spreads best while still warm. When cooking the curd, don't let it boil or the eggs will overcook.
Set a fine strainer over a medium bowl. In another medium bowl, whisk the lemon juice, sugar, and eggs until thoroughly combined and most of the sugar has dissolved.
Pour the lemon mixture in to a small nonreactive saucepan. Cook over medium heat, stirring frequently with a wooden spoon until the curd is steaming, but not boiling, and thickened and registers about 175 degrees on an instant read thermometer, 3-7 minutes.
Take the curd off the heat, add the butter, and stir until butter has melted. Pour curd through the strainer to get rid of any lumps. When cheesecake comes out of oven, pour all of the curd onto the cheesecake and use an offset spatula to spread it evenly. Let cool to room temperature and refrigerate for at least 5 hours, preferably overnight. You can refrigerate it uncovered as it will not develop a film over the curd.