In large mixing bowl, cream butter and sugar together. Beat until light and fluffy.
Add eggs one at a time. Beat well after each addition. Stir in lemon rind and vanilla. Mix baking powder in with flour-then add to butter mixture alternately with milk.
Spread evenly in greased and floured 9x13 pan. Bake at 350 degrees for 35-40 minutes.
Whisk all ingredients together.
Using a tooth pick-poke holes all over the top of the cake immediately after it comes out of the oven. Spoon mixture evenly over the top. Let cool.