Place chicken and giblets in a 4- or 5-quart enameled or stainless-steel soup pot and add water to cover. Bring to a boil, reduce to a simmer, and skim all foam as it rises to the surface. When foam subsides, simmer soup, partly covered, as you prepare vegetables.

Heat olive oil or butter in a small skillet and sauté carrot, celery, and onion until they soften and begin to turn light golden brown, about 7 minutes.

Add to simmering soup along with garlic, lentils, tomatoes, and all spices. Simmer gently but steadily, partly covered, for 1 to 1½ hours or until chicken is falling from bone and lentils are disintegrating. To prevent scorching, stir frequently and add water as soup thickens. Remove chicken and reserve dark meat for another use. Trim breast meat from skin and bones, dice or shred, and return to the soup. Adjust seasonings.

The soup can be prepared ahead up to this point and stored, covered, in the refrigerator for 1 day. Add water during reheating to prevent scorching.

If adding vermicelli, do so 15 minutes before serving and simmer in soup. Garnish each portion with parsley and/or cilantro and pass lemon wedges at the table. Rice should be served on the side, in a small dish, to be eaten along with the soup. Do not serve rice if soup contains vermicelli.