MELT butter in a pot over medium-high. Add carrots. Cook, stirring often, until softened, 8 to 10 min. Stir in broth, water and lentils. Boil, then reduce heat to medium-low. Simmer, covered, until lentils are very tender, about 25 min.
USING a hand blender, whirl soup with sour cream and salt until smooth. Serve with additional sour cream, if desired.