I know someone who inherited this name and she absolutely does not like it. You cannot get away from the "dog" references, even now. It's such a shame because its beautiful.
The etymologist Anatoly Liberman says that the root of the word "lass" seems to have meant "rag." If you care about name origin, it might not be a good idea to name someone "Lassie," especially now that it's associated with a dog as well.