Preheat oven to 350°. Spray 3 (9-inch) round cake pans with nonstick baking spray with flour. Line the bottoms of pans with parchment paper; spray again with baking spray.
In a large bowl, beat butter and sugar at medium speed with an electric mixer until light and fluffy, stopping occasionally to scrape sides of bowl.
In a medium bowl, sift together flour, baking powder, and salt. Add flour mixture to butter mixture in thirds, alternately with milk, beginning and ending with flour mixture. Add vanilla, beating to combine.
In a large bowl, beat egg whites at high speed with an electric mixer just until stiff peaks form. Fold egg whites into batter. Divide batter evenly among prepared pans.
Bake until a wooden pick inserted in the center of layers comes out clean, approximately 24 minutes. Let layers cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.
Spread Lane Cake Filling between cake layers, spreading almost to the edge. Spread Lane Cake Frosting on top and sides of cake.