Preheat the oven to 375 degrees F (190 degrees C). Sift together the flour, cream of tartar, baking soda and salt; set aside.
In a large bowl, cream together the butter, oil, confectioners' sugar and white sugar until well blended. Stir in the eggs, vanilla and lemon extracts. Gradually mix in the dry ingredients until well blended. Roll the dough into walnut sized balls. Place the cookies 2 inches apart onto the cookie sheet. Flatten cookies to 1/8 inch thickness using the bottom of a glass dipped in sugar. Colored sugar may be used if you do not plan to frost cookies later.
Bake for 9 to 12 minutes in the preheated oven, or until the edges are golden brown. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.