Preheat oven to 350°F. Line a 9x13” pan with foil and spray with cooking spray.
Cream butter, brown sugar and granulated sugar in the bowl of an electric mixer fitted with a paddle attachment. Add eggs, vanilla, and lemon juice and beat until combined. Add lemon zest, baking powder, salt, and flour and mix.
Press into prepared pan (dough is sticky, spray your hands with cooking spray to avoid it sticking to your hands).
Bake for about 16-20 minutes. (Be careful not to overcook - the center will still be jiggly when you take these out of the oven and they will finish cooking and firming up as they cool.) Cool completely before frosting.
To make frosting: cream butter with a hand mixer until smooth. Slowly mix in the the powdered sugar and salt, then add lemon juice and mix until smooth, adding more as needed for desired consistency. Frost the cooled bars, then cut into squares.
Store in an airtight container in the refrigerator for up to 3 days or freeze in a single layer for up to 1 month.