Preheat oven to 325 degrees.
In a large mixing bowl, whisk together olive oil, granulated sugar, lightly beaten eggs, greek yogurt, lemon juice, vanilla extract, lemon zest and lemon extract.
In a separate bowl, sift flour, baking soda, baking powder, and salt.
Add the flour mixture to the wet mixture while whisking together until well combined.
Add lemon cake batter to a greased 9 x 5 inch loaf pan and bake in oven for 45-55 minutes or until a toothpick is inserted in the center and comes out clean (mine baked in about 52 minutes).
Let cool for 10 minutes then remove from the loaf pan to finish cooling.
Once the cake has cooled completely, whisk together confectioner's sugar and milk or lemon juice and pour over the cake.
Let the icing set and then enjoy!