Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add eggs, 1 at a time, beating after each addition. Add lemon rind and next 2 ingredients, mixing well.
Combine flour and next 3 ingredients; add to butter mixture, beating just until dry ingredients are moistened.
Turn dough out onto a lightly floured surface; lightly flour hands, and knead in cranberries, cherries, orange rind, and almonds.
Divide dough in half; shape each portion into a 14- x 2-inch log on a lightly greased baking sheet. Flatten logs slightly.
Bake at 325° for 30 to 35 minutes or until golden brown. Cool on baking sheet 5 minutes. Transfer to a wire rack to cool completely.
Cut each log diagonally into 1/2-inch-thick slices with a serrated knife using a gentle sawing motion, and place slices on ungreased baking sheets.
Bake at 325° for 10 minutes; turn cookies over, and bake 10 additional minutes. Remove to wire racks to cool.
NOTE: If you can't find dried cranberries and cherries at your supermarket, substitute raisins, dates, or chopped dried apricots.