In a large bowl, use an electric mixer to cream together the butter, shortening, and sugar. Mix in lemon juice, lemon zest, and vanilla. In a separate bowl, whisk together the baking power and baking soda with the flour. Slowly beat in the dry ingredients with the wet mixture. The dough should come away from the sides of the bowl. Roll the dough into a log, and wrap it with plastic wrap to place in the refrigerator for 30 minutes.
Preheat the oven to 350 degrees.
Slice ¼-inch cookies, and shape into half-circle "smiles." Place cookies on a baking sheet lined with parchment paper.
Bake for around 9 minutes. Cool on a wire rack. Dust the cookies with icing sugar before serving.