In a food processor or bowl, whirl or stir flour, sugar, and salt to blend. Add butter; whirl or cut in with a pastry blender until mixture resembles coarse meal.
In a bowl, whisk the egg, vanilla, lemon peel, and lemon juice to blend. Add mixture to food processor or bowl with flour-butter mixture; whirl or stir until the dough forms a ball.
Divide dough in half. Stir apricots, citron, cherries, and walnuts into one half. Roll each half between sheets of cooking parchment into an even 8- by 16-inch rectangle, then stack the rectangles and chill until firm, about 2 hours.
Peel off the top sheet of parchment from each dough rectangle. Brush the plain dough very lightly with water. Invert the fruit dough over the plain dough. Lightly press together to seal. Remove the top sheet of parchment. Trim the edges even. If necessary, let the dough stand just until pliable. Beginning with a long side, roll into a cylinder, pulling paper from dough as you roll. Discard parchment. Cut cylinder in half crosswise. Wrap each half in plastic wrap; freeze until firm, about 30 minutes, or up to 2 weeks.
Unwrap half the dough at a time; with a thin, sharp knife, cut into 1/8-inch-thick rounds. Place 1/2 inch apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets.
Bake cookies in a 350° oven until pale golden, 12 to 14 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. With a wide spatula, transfer cookies to racks to cool completely.
Note: Nutritional analysis is per cookie.