Combine flour, baking soda, baking powder and salt in a bowl. Use a mixer to blend together the eggs, sugar, butter, vanilla, lemon extract and lemon juice in a medium bowl. Pour wet ingredients into the dry ingredients and blend until smooth. Add oil and mix well. Pour batter into a well greased 9x5-inch loaf pan. Bake at 350 degrees for 45 minutes or until a toothpick stuck into t=center of the cake comes out clean.
Make the lemon icing by combining all the icing ingredients in a small bowl mixing well. When the loaf is cool, remove it from the pan and frost the top with the icing. Let the icing set up before slicing.