Preheat oven to 350 degrees F (175 degrees C). Spray two 8-inch pans with cooking spray and lightly flour sides and bottoms.
Mix cake mix, water, egg whites, and oil in a large bowl until thoroughly combined. Divide batter between pans.
Bake cakes in the preheated oven until a toothpick inserted in the center comes out clean, 25 to 30 minutes. Cool on wire racks, about 15 minutes. Remove cakes from pans and let cool completely, about 30 minutes.
Mix vanilla frosting, whipped topping, and grated lemon peel together in a bowl.
Place 1 cake on a serving plate, coat with 1/2 the frosting, arrange raspberries on top. Cover with the second cake and frost completely.