Preheat oven to 350°F. Line a 9-inch square baking dish with parchment paper and lightly coat all sides and bottom with nonstick cooking spray.
Whisk together the powdered sugar, sugar, lemon zest, flour, and salt in a large bowl.
Add the butter cubes and cut the butter into the flour using a pastry cutter until the mixture starts to form sandy crumbs.
Press the crust mixture evenly into bottom of prepared baking dish. Bake in the preheated oven until the crust starts to turn golden brown, 25 to 30 minutes. Allow the crust to cool slightly.
While the crust is baking, prepare the filling by whisking together the lemon juice, granulated sugar, flour, and salt in a large bowl.
Add the eggs and whisk until combined.
Spread the cranberry sauce over the cooled crust.
Gently and evenly pour the lemon mixture the cranberries.
Return the pan to the oven and bake at 350 degrees until the lemon mixture is set and jiggles only slightly in center, 43 to 45 minutes.
Transfer the bars to a wire cooling rack and let cool completely, about 1 hour.
Transfer the cooled bars to the refrigerator and refrigerate 12 hours. Garnish with additional powdered sugar before slicing and serving.