Saute carrots, onion, garlic, and celery with 2 tablespoons vegetable oil in a pot over medium heat until tender, about 20 minutes. Add turmeric and cumin and saute for 3-4 minutes.
Then add red lentils, chicken broth, water, diced tomatoes, crushed tomatoes, coconut milk, salt and pepper. Cover the pot and bring to a boil. Reduce heat to medium and simmer for 25-30 minutes, until lentils are tender.
Remove the soup from the heat. Puree half of the soup in a blender until smooth. Return the pureed half of the soup back to the pot and mix well. Add the lemon juice and cook for 10 minutes. If soup is too thick, add more water. Garnish with basil and red pepper flakes and serve warm.