Pour 2 tablespoons water into a large soup pot and set over medium-high heat. Add the carrots, onion, celery, curry powder, salt (starting with 1 teaspoon), allspice, and chipotle powder. Cook for 7–8minutes, until the onion and carrot have softened, adding more water if the veggies are sticking.
Add the lentils, 4 cups water, and coconut milk and stir. Increase the heat to high to bring the soup to a boil, then reduce the heat to low, cover, and simmer for 15–20 minutes, stirring once halfway through, until the lentils are fully softened.
Add 3 tablespoons lemon or lime juice. Use an immersion blender to puree the soup to your desired consistency. Alternatively, you can transfer the soup in batches to a blender and puree. Taste and add extra salt and lemon juice if needed. Divide the soup into bowls and serve sprinkled with cilantro and a pinch of allspice and/or chipotle powder, if desired.