Preheat the oven to 350 degrees F, and line a cookie sheet with parchment paper.
Sift together the flour, baking powder and salt in a small bowl.
In a large bowl, cream together egg and 1/2 cup of granulated sugar.
Add the butter to the egg mixture and beat until fluffy.
Mix in powdered sugar, oil, lemon juice and zest until well combined.
Slowly mix the dry ingredients into wet ingredients until a dough forms.
Shape the dough into 1-inch balls, and roll in a small bowl of granulated sugar.
Once the cookie dough ball is coated completely in sugar, place 12 balls on a cookie sheet 2 inches apart (it's best to bake each batch separately).
Use a fork to flatten each cookie, making a criss-cross pattern.
Bake for 10 to 12 minutes.
Allow the cookies to cool for 2 - 5 minutes before removing from the baking sheet to a wire rack to cool completely.