Cream shortening and butter; gradually add sugar, beating mixture well.
Sift together flour, baking powder, and salt; add to creamed mixture alternately with milk, beating well after each addition. Stir in vanilla.
Beat egg whites (at room temperature) until stiff peaks form; fold into batter.
Pour batter into 3 greased and floured 9-inch round cake pans; bake at 350° for 20 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes; remove layers from pans, and let cool completely. Spread Lemon Filling between layers; frost top and sides with Fluffy Frosting, and sprinkle with coconut.