It’s an interesting question. I don’t know if there’s any evidence of wolf domestication by Neanderthals. If they didn’t domesticate them, it would be interesting to try to work out why – maybe there’s a subtle difference in psychology between H. Sapiens and H. Neanderthalensis that enabled us to bridge that gap but not them?
There isn't a whole lot of evidence for how Neanderthals lived. We have only discovered remnants of 400 Neanderthals (about 30 mostly-complete skeletons).
