Cream butter in a large mixing bowl; gradually add sugar, beating well. Add eggs, one at a time, beating well after each addition. Stir in lemon rind and juice and lemon extract.
Dissolve soda in milk, stirring well. Sift together flour and baking powder in a medium mixing bowl; gradually add to creamed mixture alternately with milk mixture, beginning and ending with flour mixture. Stir well after each addition. Cover and chill at least 1 hour.
Divide dough in half, keeping one half chilled until ready to use. Turn half of dough out onto a well-floured surface, working additional flour into dough, if necessary. Roll to 1/8-inch thickness, and cut with assorted cookie cutters.
Place on greased cookie sheets, and bake at 325° for 15 minutes. Cool slightly on cookie sheets. Remove from cookie sheets, and cool completely on wire racks. Repeat procedure with remaining dough.