Peel the leeks and remove the ends that are very dark green in color. Cut them into lengths of 8-10 centimeters. Place the oil, leeks, and water into a saucepan. Add salt and sugar. Cook slowly. When cooked, allow to cool. Pour a well beaten egg over the leeks. Mix well. When it has cooled off, blend in the juice of half a lemon. This dish is served cold.