Butter a loaf pan and set aside. In a stand mixer, cream the butter and sugar together until light and fluffy. Add the eggs one at a time, making sure each egg is well incorporated before adding the next. Scrape the sides of your bowl once or twice during mixing. Add the vanilla, lemon zest and lemon juice and mix to combine. Mix together the baking powder and flour, then add to the creamed butter mixture and mix until well combined. Pour the batter into your loaf pan and bake in a 350 degree oven for about 50 minutes or until a skewer inserted in the middle comes out clean. Cool the cake in the pan. Once the cake is completely cooled, glaze with lemon icing. Cake will keep for a week in the refrigerator.
Mix together the sugar and lemon juice until smooth. Glaze once the cake is cooled.