Step 1) Beat butter and sugar in a large bowl with mixer at medium speed, until light and fluffy. Beat in oil, eggs, vanilla and lemon juice. Blend in flour, baking powder and salt.
Step 2) Shape dough into 2 balls; wrap tightly in plastic wrap and refrigerate at least 1 hour or until easy to handle.
Step 3) Preheat oven to 375°F. Spray cookie sheets with cooking spray.
Step 4) Roll dough 1/4-inch thick on floured work surface. Use cookie cutters to cut into desired shapes; place on cookie sheets and sprinkle with sugar. OR form dough into 1-inch balls; place on cookie sheets. Flatten balls with bottom of a glass dipped in sugar.
Step 5) Bake 6 to 7 minutes for soft cookies OR 9 to 10 minutes (and golden around edges) for crispy cookies. Immediately remove from cookie sheets and cool on racks. Decorate as desired.