Preheat oven to 350° F. Butter an 8-inch square pan. Add a layer of parchment paper to the pan, leaving the edges long enough to lift the blondies out of the pan once cool for easier slicing. Butter the parchment paper, pressing it to adhere smoothly to the pan.
In the bowl of a standing electric mixer fitted with the paddle attachment, mix sugar, salt, and lemon zest until well combined and fragrant. Add butter and beat until light and fluffy.
Add eggs, one at a time, mxing well to combine. Mix in lemon juice.
Add flour and stir until just combined. Scrape batter into the prepared pan, spreading evenly to the edges. Bake until the surface of the blondies springs back when pressed gently with a finger, about 25 to 30 minutes. Cool completely in the pan.
For the frosting, beat the butter in the bowl of a standing electric mixer until light and creamy. Add confectioners' sugar, lemon juice, and salt. Mix slowly with the paddle attachment to combine, and then increase speed to medium-high and beat until well combined. Add additional powdered sugar or lemon juice, as needed, to achieve a smooth, creamy consistency.
Remove cooled blondies from the pan and top with frosting, spreading it evenly to the edges. Slice in 2-inch squares with a sharp knife, wiping the blade between slices to keep the edges of the blondies looking neat and tidy. If desired, top with lemon wedges. Set lemon wedges on a paper towel briefly to absorb excess juice before adding them to the blondies.