Red Lentil Soup with Chicken

Name: Red Lentil Soup with Chicken
Ingredients: One 3½- to 4-pound chicken, quartered, with all giblets except liver; 10 cups water, or as needed; 2 tablespoons olive oil or unsalted butter; 1 medium carrot, diced; 2 celery stalks, diced; 1 medium onion, chopped; 1 garlic clove; 1½ cups red lentils, rinsed in 2 changes of cold water; ½ cup canned crushed tomatoes; Pinch of ground ginger, or to taste (optional); Pinch of ground saffron (optional); 1/8 teaspoon harissa (Moroccan chili paste), or ¼ teaspoon dried red pepper flakes (optional); Salt, to taste; Black pepper, to taste; 1 cup broken-up vermicelli, in 1- to 1½-inch, lengths (optional); Chopped fresh parsley and/or cilantro (coriander); Lemon wedges; Cooked rice