Melt the butter in a large saucepan. Add the shallots, carrots, celery and chicken and cook over a low heat, stirring occasionally, for 8 minutes. Thinly pare the lemons and blanch the lemon rind in boiling water for 3 minutes. Squeeze the juice from the lemons.
Add the lemon rind and juice to the pan, together with the chicken stock. Bring slowly to a boil over low heat and simmer for 40 minutes, stirring occasionally.
Add the spaghetti to the pan and cook for 15 minutes. Season to taste with salt and white pepper and add the heavy cream. Heat through, but do not allow the soup to boil or it will curdle.
Pour the soup into a tureen or individual bowls, garnish with the parsley and half slices of lemon and serve immediately.