Heat oil in a soup pot over medium heat. Add onion; cook until translucent, about 3 minutes. Add celery and garlic; cook for 5 minutes more. Add vegetable stock, yam, potato, lentils, curry paste, salt, and pepper. Bring to a boil. Reduce heat and simmer until potatoes are cooked, 15 to 20 minutes.
Stir coconut milk into the pot with the vegetables. Transfer half of the soup to a large bowl. Blend with a stick blender. Return blended soup to the pot and stir in cilantro.