In mixing bowl cream together granulated sugar, butter, and 1 teaspoon lemon peel till fluffy.
Add eggs, one at a time, beating well after each addition.
Stir together flour and soda; add to the creamed mixture alternately with the milk, beating after each addition.
Beat in the lemon juice.
Turn the mixture into a greased and lightly floured 13x9x2-inch baking dish.
Bake at 350° till cake tests done, about 25 minutes.
Stir together sifted powdered sugar, remaining lemon peel, and vanilla; stir in enough milk (about 2 tablespoons) to make glaze of spreading consistency.
Spread the glaze on cooled cake