Heat the olive oil in a large pan over medium heat, and saute the onion, carrots and celery until they start to soften, about 5 minutes.
Add in the garlic, cumin, cayenne, and tomato paste, and stir briefly, about 1 minute.
Add in the water, lentils, and 1 1/2 teaspoons of salt. Bring the water to a boil, then lower the heat and cover. Simmer until the lentils have expanded and are tender, about 15 minutes.
Once the lentils are tender, stir in the coconut milk and cilantro. Adjust seasoning to taste, adding more salt and some freshly ground pepper, if desired. Serve warm.
Leftovers can be stored in an airtight container in the fridge for up to a week. This soup will thicken in the fridge, but it will thin out again when it's heated. You can always add an extra splash of water, if needed, to thin it to a consistency you like again.