Preheat oven to 350 degrees F (175 degrees C). Grease and flour 13x9 inch pan. Sift together the flour, baking powder and salt. Set aside.
In a large bowl, cream together the butter and lemon zest. Add the sugar and beat until light and fluffy, about 5 minutes. Beat in the eggs one at a time, then stir in the vanilla and lemon extract. Beat in the flour mixture alternately with the milk, mixing just until incorporated.
Pour batter into prepared pans. Bake in the preheated oven for 30 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Lemon Glaze: Within 10 minutes of the finish of baking the cake, begin the glaze. Put all of the ingredients in a medium pot and bring to a boil stirring frequently. Once the galze begin to turn white and foamy stir and remove from the heat. Remove the cake from the oven and begin to immediately poke holes in the cake with a toothpick. The more wholes, the more glaze gets through the cake. Slowly pour the glaze sauce over the cake covering the holes. Allow the cake to cool completly.
To make frosting: In large bowl, beat butter and grated lemon zest together for about 2 to 3 minutes, add confectioners' sugar and lemon juice.