Bring eggs, butter and buttermilk to room temperature. Grease and flour a 10" fluted tube pan or 2 (8"x4"x2") loaf pans.
In a small bowl stir together flour and baking soda; set aside.
In a large mixer bowl beat butter with an electric mixer on medium speed until softened.
Gradually add sugar, beating until well combined.
Add eggs, one at a time, beating for 1 minute after each addition and scraping bowl frequently.
Add lemon peel, lemon juice and vanilla; beat well. Add flour mixture and buttermilk alternately to beaten mixture, beating after each addition just until combined. Turn batter into prepared pan or pans.
Bake in a 350 degree oven for 55 to 60 minutes for tube pan, 45 to 50 minutes for loaf pans, or until a wooden pick inserted near center comes out clean. Cool on a wire rack 15 minutes. Remove from pan; cool completely. Drizzle with lemon icing.
ICING: In a small bowl combine 1 cup sifted powdered sugar, 1 teaspoon finely shredded lemon peel and enough lemon juice (3 to 4 teaspoons) to make an icing of drizzling consistency. Drizzle icing over cake.
