John and Katie Varney leaving with Wally after adopting him. By Matt de Simone   When a winter storm threatened the League for Animal Protection in late January, the shelter’s safety depended not on equipment, but on people willing to step in at a moment’s notice. As freezing temperatures and icy conditions approached, shelter officials learned that the facility’s backup generator had failed — a discovery that raised immediate concerns for the dogs and cats in their care. “We realized the generator wasn’t working the very day the storm was arriving,” said Pat Shaver, who has served as shelter director...