Cream butter in a mixing bowl; gradually add sugar, beating well. Add egg; beat well.
Combine flour, baking powder, and salt; add to creamed mixture alternately with milk, beginning and ending with flour mixture. Mix well after each addition. Stir in vanilla.
Pour batter into a greased and floured 8-inch square pan. Bake at 350° for 40 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes; remove from pan, and let cool completely. Cut into 2- x 4 - inch bars. Place each bar on an individual serving plate, and spoon Lemon Sauce over top.