Preheat your oven to 350 degrees.
In a small saucepan melt the butter and oil together over low heat. Make sure the mixture doesn't fry. Let cool slightly and set aside.
In a stand mixer or with an electric mixer, mix the eggs and sugar together until combined.
Add the oil and butter and then the vanilla, lemon zest and juice.
Add the dry ingredients and mix just until the dough comes together.
Form the dough into a disc and wrap it in plastic wrap and let it rest in the refrigerator for at least an hour.
Form little discs with the dough by hand and roll them in powdered sugar. Bake for 15-20 minutes on a baking sheet lined with parchment paper or tin foil until little cracks in the tops of each cookie start to form.