Separate eggs and let stand at room temperature for 30 minutes. Preheat oven to 325 degrees.
In a large mixing bowl, stir together flour, sugar, baking powder and salt. Make a well in the center. In a medium bowl, whisk together water, oil, 4 teaspoons lemon peel, and vanilla extract. Add to center of flour mixture. Beat with an electric mixer on low until moistened; beat on medium - high for 5 minutes or until mixture is satiny smooth.
Thoroughly wash the beaters. In another mixing bowl, beat egg whites and cream of tartar on medium - high until stiff peaks form (tips stand straight). Fold egg whites into the batter.
Spoon batter evenly into an ungreased 10 - inch tube pan. Cut through batter with a knife to remove air pockets. Bake for 50 to 55 minutes or until cake springs back when lightly touched. Immediately invert pan and cool completely, about 1 hour.
Run a knife around side and center tube of pan. Remove cake to a serving plate. Pour lemon frosting over top, letting frosting drip down side of cake.
Lemon Icing: In a small mixing bowl, beat 1/3 cup butter until fluffy. Gradually add 2 cups of powdered sugar, beating well. Slowly beat in 1/4 cup lemon juice and 4 teaspoons grated lemon peel. Slowly beat 1 cup powdered sugar. Makes 12 servings.