Preheat oven to 350 degrees F. In a mixing bowl, cream butter, lemon juice, and confectioners' sugar. Add the eggs, one at a time, beating well after each addition. Beat in lemon extract, milk, and lemon peel.
Combine flour and baking soda; gradually add to the creamed mixture. With a spoon, drop cookies 1 in. apart on ungreased baking sheets.
Bake at 350 degrees F for 8-10 minutes or until lightly browned on bottom. Let sit for 5 minutes then remove to wire racks to cool. When cool, sprinkle with powedered sugar.