Preheat the oven to 175°C. Line a baking sheet with parchment paper.
Mix the cookie dough with the flour until it is an even texture. Turn the dough out onto the prepared baking sheet and form it into the shape of an egg about 1/2-inch thick, 9 inches long and 7 inches wide at its widest point. Bake until golden around the edges, about 25 minutes. Remove the cookie from the oven to cool, about 15 minutes.
Meanwhile, beat the egg whites and sugar with an electric mixer until combined. Add the lemon juice and continue to beat until thick and glossy, about 5 minutes.
Fill a pastry bag or plastic baggie with the icing, snip off a small corner and pipe decorations on the cookie. Attach the candies in patterns to make a decorative Easter egg.