In a large bowl, stir together the granulated sugar, oil, and eggs. Use a box grater to zest as much of the lemon peel as you can, and then reserve 2 tablespoons of lemon juice (or as much as you can). Stir the zest and juice into the bowl.
Then, stir in the flour, baking powder, and salt until a dough ball forms. Cover and chill for at least one hour or overnight.
Divide into 12 balls and roll in powdered sugar. Place on a prepared baking sheet and bake at 350°F for 12-14 minutes until the edges just begin to brown. Remove to a cooling rack and allow to cool.
You can use olive oil or other oils you may have on hand. Just keep in mind if you use an oil with a heavy taste or color, it may slightly change the final color and taste of your cookies. These cookies will naturally turn out yellow mostly from the egg yolks and lemon zest, but if you want to bump up the yellow color more you can add a little food dye to the wet ingredients (before stirring in the flour, baking powder, and salt).