Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch pan. Sift together the flour, baking powder and salt. Set aside.
In a large bowl, cream together the butter and 1 1/2 cups sugar until light and fluffy. Beat in the flour mixture alternately with the milk, mixing just until incorporated. Stir in the 1/2 teaspoon vanilla and lemon extracts.
In a large glass or metal mixing bowl, beat 5 egg whites until stiff peaks form. Fold 1/3 of the whites into the batter, then quickly fold in remaining whites until no streaks remain.
Pour batter into prepared pan. Bake in the preheated oven for 45 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.
To make the Fluffy White Frosting: Combine 1 1/2 cups sugar, 2 egg whites, corn syrup, and cream of tartar in the top of a double boiler. Add cold water and beat on low speed of electric mixer just until blended. Place over boiling water and beat constantly on high speed about 3 minutes or until soft peaks form. Remove from heat and place over cold water. Add vanilla and beat an additional 3 minutes or until frosting is thick enough to spread.
To make the snowballs: Cut cake into 2-inch squares. Trim corners of each square, leaving rounded edges. Spread top and sides with frosting. Sprinkle coconut generously over frosting.