Cream butter and sugar in a large mixing bowl. Beat in eggs, lemon juice, and lemon zest till well combined.

Stir in flour, baking powder, and salt

Roll dough into tablespoon sized balls and place on lightly greased cookie sheets. Flatten with a glass dipped in sugar.

Bake at 350° for 9-10 minutes, or till barely light brown on the bottom. Let sit 3-4 minutes on pan, then remove to cooling racks.
Cool cookies completely, then frost. I piped frosting on with a 1M star tip.

Frosting

Beat together butter, powdered sugar, salt, lemon zest, and lemon juice in a mixing bowl till creamy, adding milk if needed. If you are piping the frosting, it needs to be thick. If you are just spreading it on, you can add more liquid.