Heat 4 tablespoons olive oil in a large Dutch oven over medium heat. Add the onion, celery, and carrot. Season with salt and cook for 5 minutes until softened.
Add the garlic, black pepper, turmeric, cumin, ginger, cinnamon, and cayenne. Cook for 1–2 minutes, stirring frequently until fragrant.
Stir in the crushed tomatoes, tomato paste, cilantro, green lentils, red lentils, and chickpeas. Season lightly with salt and cook for 5 minutes.
Pour in the vegetable stock and raise the heat. Bring to a boil for 5 minutes, then reduce heat to low, cover, and simmer for 45 minutes, stirring occasionally. Add more stock or water as needed to keep the soup thick but pourable.
Stir in the rice and cook for an additional 15 minutes, or until the rice and lentils are fully tender. Adjust salt to taste.
Serve hot with fresh lemon wedges.