Mix flour, baking powder and salt. In a medium-sized saucepan, melt butter and margarine over moderate heat. Stir in granulated sugar; remove from heat and let cool 15 minutes. Beat in eggs and lemon extract.
Add flour mixture, one-fourth at a time, mixing well after each addition. Wrap dough and refrigerate 1 to 2 hours, or overnight.
Heat oven to 375 degrees F. Divide dough in half. On a floured board or pastry cloth or between two layers of waxed paper roll one piece of dough 1/8" thick. Cut with assorted cookie cutters. Place cookies two inches apart on ungreased baking sheets.
Decorate with icing or colored sugar if desired. Repeat with remaining dough.
Bake 8 to 10 minutes, until edges are lightly browned. Cool on wire racks.