In a large mixing bowl, cream together the softened butter, sugar, and confectioners sugar until light and fluffy.

Gradually add the vegetable oil and mix until well combined.

Beat in the eggs one at a time, then stir in the lemon extract.

In a separate bowl, whisk together the all-purpose flour, baking soda, and cream of tartar.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. The dough will be stiff.

Roll the dough into 1-inch balls.

Place the dough balls 2 inches apart on ungreased baking sheets.

Press the bottom of a glass dipped in water, then into additional sugar, and gently press each cookie.

Bake in a preheated oven at 350°F (175°C) for 10 minutes, or until the edges are lightly browned.

Remove from oven and let cool completely on baking sheets before serving.