In a large bowl, cream butter and confectioners' sugar until light and fluffy; beat in lemon juice. Combine flour and cornstarch; gradually add to the creamed mixture and mix well. Shape into two 8-in. rolls; wrap each roll in plastic wrap. Refrigerate for 2 hours or until firm.
Unwrap and cut into 1/4-inch slices. Place 2 in. apart on ungreased baking sheets. Bake at 350° for 8-12 minutes or until the cookies are firm to the touch. Remove to wire racks to cool.
For frosting, in a small bowl, beat the butter and confectioners' sugar until smooth. Stir in the lemon juice, lemon peel and food coloring. Frost cooled cookies.