Lugh was the first wolf in the wild to treat Ghost with kindness after she escaped from captivity, despite being am aggressive wolf something about the wary black and white she-wolf had drawn him to her, and he hasn't left her side since.
Lugh acts as the alpha's enforcer and Bolverik (punisher) protecting Ghost and helping with the running of the pack, things like organizing hunts, and disciplining rebellious wolves, but he always waits for the last word from his mate and values her assistance with tough decisions. He has no desire to be alpha, as running the pack would be too much hassle for a single minded hunt focused wolf like Lugh.