In a large bowl, cream butter and sugar until light and fluffy. Beat in eggs, milk and lemon extract.
In a separate bowl, combine the flour, baking powder, salt and baking soda. Gradually add the dry ingredients to the creamed mixture and mix well. Cover and chill for 2 hours.
Preheat oven to 350°F.
Roll dough out on a lightly floured surface to 1/8-inch thickness. Cut with a 2-inch cookie cutter dipped in flour. Place 2-inches apart on ungreased baking sheet.
Bake for 8-10 minutes or until the edges just begin to brown. Allow cookies to cool for 3 minutes on the baking sheet before transferring to wire racks to cool completely.
In a medium bowl, whisk together the powdered sugar and lemon juice until smooth. Dip each cookie top into the glaze. Return to the wire rack, glaze side up. Let cookies set until icing has set.