Using an electric mixer, cream together the butter, shortening and sugar. Mix in the 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 be evenly combined and come away from the sides of the bowl.
Roll the dough into a 12 inch log, wrap it with plastic wrap and place in the fridge a minimum of 2 hours.
After the 2 hours of chilling, the log should be firm and ready to be sliced. Slice into 1/4 inch cookies and place on a cookie sheet lined with parchment paper.
Bake in a 350F oven for 8-10 minutes. Cool on a wire rack.
Dust the tops of the cookies with icing sugar before serving.