Sift the sugar and the flour together in a large bowl. Whisk in the eggs, lime juice, and lime zest. Whisk until completely combined.
Pour carefully over the warm crust and return to the oven. Bake the bars for 22-25 minutes or until the center is set and no longer jiggly. Test by tapping the side of the pan.
Remove the bars from the oven and allow them to cool completely at room temperature (about 2 hours). Once cooled to room temperature, place the bars in the refrigerator to chill for another 2 hours.
When you are ready to cut the bars, pull up on the parchment paper and place the bars on a cutting board. Using a knife, cut the bars, wiping the knife off with a damp paper towel after each slice. Return to the refrigerator until ready to serve.
Optional - Dust with confectioners' sugar before serving (See notes)
Store leftovers in the refrigerator for up to 1 week.