Preheat oven to 350 F. Make crust: put butter, flour, confectioners’ sugar, 2 tsp lemon zest, and the salt in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until well blended. Transfer mixture to a 9-by-13-inch rimmed baking sheet. Press batter evenly into baking sheet. Chill in freezer 10 minutes. Bake until golden, 20 to 22 minutes. Let cool completely on a wire rack.
Make filling: Whisk together whole eggs, 1 ¾ cups plus 2 Tbsp granulated sugar, the lemon juice, and 1 Tbsp plus 2tsp lemon zest. Pour over crust. Bake until filling is set, 18 to 20 minutes. Let cool completely on a wire rack. Keep oven at 350 F. Make meringue topping: Put egg whites and ½ cup granulated sugar in the clean bowl of an electric mixer fitted with the whisk attachment. Beat on medium-high speed until stiff peaks form. Using an offset spatula or the back of a spoon, spread meringue over filling, swirling to create soft peaks. Bake until meringue begins to brown, 8 to 10 minutes. Let cool completely. Cut into bars. Bars can be refrigerated in an airtight container, up to 1 day.