MIX flour, baking powder and salt in small bowl. Cream butter, granulated sugar and powdered sugar in large bowl. Blend in oil, eggs, lemon peel and lemon extract. Stir in flour mixture. Cover and refrigerate for 2 hours.
HEAT oven to 350°F Shape dough into 1-inch balls. Place 2 to 3 inches apart on ungreased baking sheet. Flatten to 1/8-inch thickness with bottom of glass dipped in granulated sugar.
BAKE 10 to 12 minutes, or until edges are light golden brown. Remove cookies from pan immediately. Cool on wire rack.
LEMON CRISPS: Follow recipe above, except shape dough into 3/4-inch balls and flatten to 1/16-inch thickness with sugar-dipped glass. Bake 7 to 9 minutes, or until edges are light golden brown.