Cream shortening in a large mixing bowl; gradually add 1/2 cup sugar, beating until light and fluffy. Add egg; beat well. Add molasses and 1 tablespoon lemon juice, stirring well.
Sift together flour, soda, salt, cinnamon, cloves, and ginger in a medium mixing bowl; add to creamed mixture alternately with boiling water, beginning and ending with flour mixture. Stir well after each addition. Fold in chopped apple. Chill dough 1 hour.
Drop dough by teaspoonfuls 2 inches apart onto greased cookie sheets. Bake at 350° for 10 minutes. Remove from cookie sheets, and cool on wire racks.
Combine powdered sugar, butter, and remaining lemon juice in a small mixing bowl; beat at medium speed of an electric mixer until smooth. Spread evenly over tops of cooled cookies. Sprinkle each with grated lemon rind.