Melt 1 tablespoon of the butter in a medium saucepan. Add half of the shallots and cook over low heat for 2 minutes. Add the wine and thyme sprigs and bring to a boil. Add the mussels, cover and cook for 3 to 5 minutes; remove them to a bowl as they open. Strain and reserve the cooking liquid. Remove the mussels from their shells. Discard the shells.
Heat the olive oil in a medium saucepan. Add the carrots and remaining shallot and cook over low heat until softened but not browned, about 5 minutes. Add the water, clam juice, reserved cooking liquid and lentils. Cover and simmer over low heat until tender, about 1 hour.
Puree the soup in a food processor or blender. Pass it through a fine sieve set over the saucepan and whisk in the remaining 2 tablespoons of butter. Arrange the mussels in soup plates and ladle the soup over them. Sprinkle with the chives and serve.