Place 6 quart stock pot on stove. Add 4 tablespoons olive oil. Over high heat until oil shimmers. Add onion and garlic. Sauté until golden, about 4 minutes.
Stir in tomato paste, cumin, salt, black pepper, and chili powder. Sauté 2 minutes.
Stir in broth, 2 cups water, lentils, and carrots. Bring to a simmer, then partly cover and simmer on medium-low about 30 minutes, until lentils are soft.
Puree half the soup using an immersion blender or food processor. Return pureed soup to pot. Adjust salt if needed.
To serve, reheat, stir in lemon juice and cilantro. If desired, drizzle with olive oil and lightly dust with chili powder.