Preheat oven to 350°F. Line a 9x13-inch baking dish with parchment paper, leaving enough overhang on the sides to lift the bars out later.
In a large mixing bowl, beat the softened butter and powdered sugar until smooth and creamy. Add the flour and salt and mix just until a soft dough forms. Press the dough evenly into the prepared baking dish.
Bake the crust for 18 to 22 minutes, or until the edges are lightly golden.
While the crust bakes, whisk together the eggs, sugar, flour, lemon juice, lemon zest, and salt until smooth and well combined.
Pour the lemon filling over the warm crust.
Return the pan to the oven and bake for 20 to 24 minutes, or until the center is set and no longer appears wet. The filling should have only a slight jiggle in the center when the pan is gently shaken.
Place the pan on a wire rack and allow the lemon squares to cool at room temperature for about 1 hour.
Transfer the cooled pan to the refrigerator and chill for at least 2 hours, or until completely cold.
Lift the bars from the pan using the parchment paper. Dust generously with powdered sugar and cut into squares before serving.