Preheat your oven to 350 degrees Fahrenheit. Butter a 9" x 9" baking pan and set aside.
In a large mixing bowl or in the bowl of a stand mixer affixed with the paddle attachment, beat together the butter and sugar on medium speed until fluffy, about two minutes.
Add the eggs, one at a time, beating well after each addition.
Add the lemon juice and lemon zest and beat on low just until combined.
In a medium bowl, sift together the flour, baking powder, baking soda and salt.
Pour the flour mixture into the butter/sugar/lemon mixture and mix together until blended.
Spread mixture in the baking pan.
Bake for 30 minutes, until the cake bars begin to get golden brown around the edges, and are set in the middle.
Cool for about 20 - 30 minutes.
Make the glaze. Whisk together the powdered sugar, lemon juice and lemon zest.
Drizzle glaze over the top of the cake bars. Cut into squares and serve.
