Preheat oven to 350 degrees F ( 175 degrees C ). Grease cookie sheets.
In a medium bowl, stir together the flour, sugar, baking soda, salt, and lemon zest. Make a well in the center and fill it with the oil, lemon juice, and vanilla. Stir everything together until it forms a dough. Alternate method: Put everything into the food processor and blend until dough forms.
Drop cookie dough by teaspoonfuls, about 2 inches apart, onto the prepared cookie sheet. Bake for 10 to 12 minutes in the preheated oven. Edges should be golden brown. For a softer cookie, bake for only 7 minutes. Cool on racks, and store in an airtight container.