Heat the oil in a large saucepan over a low heat, add the onion and cook, stirring occasionally, for 10 minutes or until softened but not browned.
Tip the lentils into the pan and pour in the water and vegetable stock. Bring to the boil. Add the carrot and celery. Bring back to the boil, then cover and simmer for about 40 minutes or until the lentils and vegetables are very tender.
Purée the soup, either in a blender or food processor, or using a hand-held blender directly in the pan. Reheat until the soup is piping hot, but not boiling. Remove the pan from the heat.
Stir in the blue cheese and chives. Ladle into soup bowls, season with pepper, garnish with the celery leaves, then serve while hot.