In a large mixing bowl with a hand mixer or in a stand mixer with a paddle attachment, cream together the butter, vegetable oil, and sugar until fluffy and pale in color.
Add in the eggs, vanilla, and sour cream and mix until combined.
Add the baking powder, salt, and flour (one cup at a time), mixing until everything is evenly incorporated.
Cover and chill the dough – preferably overnight for best results.
Preheat the oven to 350 F. On a lightly floured surface roll the dough out to a ¼ or ½ inch thickness.
Cut into holiday shapes with a cookie cutter.
Transfer cookies to a lightly greased cookie sheet and bake for 10 minutes. Remove from oven and move cookies to a rack to cool.
In a large mixing bowl with a hand mixer or in a stand mixer with a paddle attachment, cream the butter until fluffy.
Add the confectioners’ sugar, 1 cup at a time, and mix until combined.
Add the salt, egg whites, vanilla and lemon juice and beat until ingredients are incorporated.
Spread over cooled cookies, sprinkle with colored sugar, and serve immediately.