In a mixer, combine butter, sugar and vanilla. Add lemon peel, lemon juice, then beat. Slowly add in flour--mix well. Shape the dough into balls using one teaspoonful for each cookie. Dip one side of each ball in the chopped nuts. Place the cookies on a greased cookie sheet (nut side up). Flatten each cookie with the bottom of a glass. Bake at 350 degrees for 22-25 minutes. Remove from oven and cool.
Drizzle each cookie with the following glaze - 1 cup sifted powdered sugar, 3-4 tsp. of lemon juice--stir by hand in a bowl--should have a runny consistency.