Preheat oven to 350 degrees.
In a medium-sized mixing bowl, combine flour, baking soda, and salt.
In a large mixing bowl, cream together butter, vegetable oil, sugar, powdered sugar, and water. Add in eggs and lemon juice. Mix until combined.
Slowly add in flour mixture until combined.
Roll the dough into 2 inch sized balls onto a nonstick cookie sheet.
Add the rough edge by dipping the bottom of a glass into regular sugar and flatten the cookie. The cookie should be about 1/2 an inch thick.
Bake cookies for 8-10 minutes.
Cool on a rack before icing.