For the crust: Preheat the oven to 350 degrees F. Grease a 12-inch tart pan with removable bottom with some oil.
Pulse the butter, sugar, salt and cookies in a food processor until combined. Firmly press the crumb mixture into the prepared tart pan (the mixture will come only halfway up the sides). Bake until golden brown, about 10 minutes. Let cool completely.
For the filling: In a heavy saucepan, whisk together the sugar, cornstarch and salt. Add the milk and 1 cup water and continue to whisk until the cornstarch is dissolved. Cook over medium-high heat, whisking, until the mixture comes to a boil, 3 to 5 minutes; it will start to thicken to a custard-like texture.
In a medium bowl, whisk together the egg yolks. Gradually mix the yolks into the thickened cornstarch mixture in the saucepan. Continue to whisk until combined, then remove from the heat. Whisk in the butter and lemon zest and juice. Let cool slightly, then whisk in the tequila. Cover the filling with plastic wrap and set aside.
For the meringue: With an electric mixer in a large bowl, beat the egg whites with the cream of tartar and a pinch of salt until soft peaks form, 2 to 3 minutes. On slow speed, gradually add the sugar and continue to beat until stiff peaks form, another 1 to 2 minutes.
Pour the filling into the tart pan and spread over the crust. Pipe dollops of the meringue with peaks all atop the filling in circles. Bake until the meringue peaks turn light brown, about 15 minutes. Let cool to room temperature, about 30 minutes. Chill the tart until completely set, about 1 hour.