Heat olive oil in a large pot over medium-high heat. Add onion, carrots, and celery. Sauté until softened, 8–10 minutes.
Stir in garlic, cumin, and tomato paste. Cook for 1 minute, until fragrant.
Add water, lentils, and salt. Bring to a boil, then reduce the heat, cover, and simmer for about 15 minutes, until the lentils are tender.
Stir in coconut milk, cilantro, and lemon juice. Adjust seasoning with additional salt or pepper to taste.
Serve warm, garnished with extra fresh cilantro if desired.