Preheat oven to 350°F (175°C). In a mixing bowl, cream together the softened butter and sugar until light and fluffy. Add the flour and salt, mixing until a crumbly dough forms. Press the dough evenly into a greased or parchment-lined 9x13-inch baking dish. Bake for 18–20 minutes, or until the edges are lightly golden. Remove and set aside.
While the crust bakes, whisk together sugar and flour in a large bowl. Add the eggs, lemon juice, and zest. Whisk until completely smooth and well combined. The mixture should be slightly thick but pourable.
Pour the lemon mixture over the pre-baked crust. Return to the oven and bake for another 18–20 minutes, or until the center is just set and no longer jiggly. Let the bars cool completely at room temperature before transferring to the refrigerator.
Once chilled, dust the top with powdered sugar. Slice into 16 even squares or rectangles using a sharp knife. Wipe the blade between cuts for clean edges.