Preheat oven to 350 degrees F. Line cookie sheet with parchment paper.
Beat butter and 1 cup of the sugar and the powdered sugar.
Slowly add oil, lemon juice, lemon zest and eggs.
Combine well.
Add flour, salt, baking soda, cream of tartar until a dough forms.
Roll into 1 inch balls and place on parchment paper.
On a plate, pour ¼ c of sugar.
Use the bottom of a glass and dip it in the sugar then into the dough ball to flatten it a bit. The thinner, the crisper.
Bake8-10 mins.
Keep chilled.