Preheat oven to 350° F. Grease a 9×13-inch baking pan, then set aside.
Beat butter and sugar together in a mixing bowl. Add well-beaten eggs and mix together with the butter and sugar. Add the lemon zest, milk, flour, salt*, and baking powder to the mixing bowl and mix everything together well. Pour batter into baking pan. Bake at 350° F. for 40 minutes or until cake tests done. Cool completely before adding glaze.
Add lemon juice into a bowl and slowly whisk in powdered sugar, half a C. at a time until thick enough to spread over cake. Pour over the top of cooled cake and use a knife to spread evenly over cake, letting the icing drip over sides of cake.