Preheat the oven to 350°F. Line a 9x13 baking pan with parchment paper, leaving an overhang on all sides. Lightly spray with nonstick cooking spray.
In a food processor, combine flour, sugar, and salt. Add cold butter and pulse until the mixture is crumbly and just begins to come together.
Press the mixture evenly into the prepared pan. Bake for 13 to 15 minutes, until very lightly golden. Remove from oven.
While the crust bakes, sift the sugar and flour together in a large bowl. In a separate bowl, whisk the eggs, then strain them through a fine-mesh sieve into the sugar and flour mixture. Whisk to combine, then whisk in the lemon juice and zest.
Pour the filling over the warm crust. Return to the oven and bake at 325°F for 22 to 26 minutes, until the center is set and no longer jiggles when the pan is tapped.
Cool completely at room temperature, about 2 hours. Refrigerate for at least 1 hour before slicing.
Lift the bars from the pan using the parchment overhang. Dust with powdered sugar, slice into squares, and serve chilled. Wipe the knife clean between cuts for neat edges.