Preheat oven to 350 degree F. Grease a 13x9x2-inch baking pan. Line the bottom with waxed paper. Set aside.
Place the 1 cup sugar and eggs in a 3- to 4-quart heatproof mixing bowl. Place bowl over 1 to 2 inches hot water in a large saucepan (bowl should not touch water). Heat over low heat, stirring occasionally, for 5 to 10 minutes or until egg mixture is lukewarm (105 degree F to 110 degree F). Remove bowl from saucepan. Add the first 1 tablespoon lemon juice and vanilla.
Beat egg mixture with electric mixer on high speed for 10 minutes. Sift about one-third of the flour over egg mixture. Gently fold in flour. Repeat sifting and folding in one-third of the flour at a time. Gently fold in melted butter and lemon peel. Spread batter into prepared pan.
Bake in preheated oven for 25 minutes or until a wooden toothpick inserted near the center of the cake comes out clean. Cool cake in pan on a wire rack for 10 minutes. Remove cake from pan; peel off paper. Cool thoroughly on rack.
Combine the 4-1/2 cups granulated sugar, the water, and cream of tartar in a 3-quart saucepan. Bring mixture to boiling over medium-high heat, stirring constantly until sugar dissolves. Reduce heat to medium-low. Clip a candy thermometer to side of the saucepan. Cook until thermometer registers 226 degree F, stirring only when necessary to prevent sticking. Mixture should boil at a moderate, steady rate over the entire surface (this should take about 15 minutes). Remove saucepan from heat. Cool sugar mixture at room temperature, without stirring, to 110 degree F (allow about 1 hour). Stir in the 1 tablespoon lemon juice. Stir in enough powdered sugar to make icing that is easy to drizzle. If necessary, beat the icing with a rotary beater or a wire whisk to remove any lumps. If the icing gets too thick to drizzle, beat in a few drops hot water.
Using a serrated knife, trim sides and top of cake to make the edges smooth and straight. Cut cake into 1-1/2-inch squares, diamonds, triangles, and/or circles. Brush off crumbs. Place the cake pieces on wire racks with waxed paper underneath.
Insert a 2- or 3-prong, long-handled fork into the side of one cake piece. Holding the cake over the saucepan of icing, spoon on enough icing to cover sides and top. Place frosted cake piece back on the wire rack, making sure it doesn't touch other cake pieces. Repeat with remaining pieces. Let cakes dry 15 minutes. Repeat with a second layer of icing, except set cake pieces on top of the fork prongs (do not spear them). Repeat with a third layer of icing. If necessary, reuse the icing that has dripped onto the waxed paper, straining to remove crumbs. Tint any remaining icing with food coloring as desired and pipe or drizzle atop cakes. Makes about 48.