Preheat the oven to 350 degrees F.
For the crust: Pulse the cookies, sugar and zest in a food processor until fine. Pulse in the melted butter until the crumbs are moist. Press into a 9-inch pie pan and bake until golden and set, 8 to 10 minutes. Set aside to cool.
For the filling: Whisk together the sugar and egg yolks in a heavy-bottomed pot until the sugar is completely dissolved. Stir in the lemon juice. In a separate bowl, whisk together the cornstarch and 1/2 cup water and set aside. Cook the lemon mixture over medium heat, whisking constantly, until just beginning to thicken. Whisk in the cornstarch slurry and cook until it thickens. Remove from the heat and whisk in the butter. Fill the pie crust with the filling, spreading it out evenly.
For the meringue: Using a stand or electric hand-held mixer, whisk the egg whites until frothy. Add the cream of tartar and whisk again. Whisk together the sugar and cornstarch in a separate small bowl. With the machine running, add the sugar mixture a little at a time and whisk until the meringue forms stiff peaks.
Spread the meringue over the top of the warm pie, making sure to get it to the edges. Bake until the meringue is just beginning to brown, 8 to 10 minutes. Let cool completely before serving.