Preheat oven to 350 degree F. Generously grease and flour a 10-inch fluted tube pan; set aside.
In a large mixing bowl prepare cake mix according to package directions; pour batter into prepared pan. In a medium mixing bowl, beat cream cheese, butter, and cornstarch until combined. Gradually beat in sweetened condensed milk, the egg, 2 teaspoons of the lime peel, 3 tablespoons of the lime juice, and green food coloring, if desired.
Spoon cream cheese mixture evenly over batter. Bake about 45 minutes or until a wooden toothpick inserted near the center comes out clean. Cool in pan on a wire rack for 10 minutes. Remove from pan. Cool completely on wire rack.
For icing, in a small bowl stir together the powdered sugar, the remaining 1 teaspoon lime peel, 1 tablespoon lime juice, and enough water (2 to 3 teaspoons) to make of drizzling consistency. Drizzle over cooled cake. Makes 12 servings.