In a large saucepan or double boiler combine sugar, cornstarch and salt. Mix well. Beat the egg yolks and water together, then whisk into sugar mixture. Cook over medium heat, stirring constantly, until mixture is thickened. Remove from heat and stir in lemon juice and butter. Cover with plastic wrap until completely cooled.
Preheat oven to 350 degrees F (175 degrees C). Grease and flour three 9-inch pans. Sift together the flour, baking powder, and salt. Set aside.
In a large bowl, cream together the shortening and sugar until light and fluffy. Beat in the eggs one at a time, mixing until each egg is incorporated; stir in the vanilla. Beat in the flour mixture alternately with the milk. Divide batter into 3 bowls.
In the first bowl, stir in lemon zest and yellow food coloring; pour into prepared pan. In the second bowl, stir in orange zest and orange food coloring; pour into second prepared pan. In the last bowl, stir in the lime zest and green food coloring; pour into third prepared pan.
Bake in the preheated oven until a toothpick inserted into the center of each cake layer comes out clean, about 30 minutes. Let cool in pan for 5 minutes, then turn out onto a wire rack and cool completely.
Assemble the cake: stack the layers together with the Lemon Filling in between the layers. Frost sides and top with Orange Cream Frosting. Refrigerate until serving.