Preheat the oven to 350°F. Prepare an 8x8" pan by spraying with cooking spray or lining with foil, and set aside.
In a large bowl or the bowl of a stand mixer, beat together the butter, sugar, and lemon zest until light and fluffy. Add the eggs one at a time, mixing well after each addition, then add the lemon juice. Add the flour and baking powder, and mix until just combined.
Pour the batter into the prepared pan and smooth into an even layer. Bake 20-25 minutes, or until a toothpick inserted into the brownies comes out clean. Let cool for 10-15 minutes.
To make the glaze, whisk together the powdered sugar, lemon juice and zest, then pour over the brownies, spreading evenly to coat. Let cool completely before slicing and serving.
Note: If using unsalted butter, make sure to add a pinch of salt to the batter.