Using electric beaters, beat margarine, sour cream, egg, and lemon extract until smooth. Mix in sugar. Combine flour, baking soda, and salt, and gradually beat into margarine mixture. Chill dough 4 to 6 hours.
Roll dough on a floured surface to 1/4 inch thickness. Cut into shapes with 2-inch cookie cutters and lay on a baking sheet. Bake 8 to 10 minutes. Let cool on wire racks.
Make frosting by whisking together powdered sugar, lemon extract, and enough milk to make a spreadable consistency.