NEW YORK — Sears will live on– at least for now. The company’s chairman and largest shareholder, Eddie Lampert, won a bankruptcy auction for Sears, averting liquidation of the iconic chain, according to a source familiar with the negotiations. The person agreed to speak on condition of anonymity because they were not authorized to discuss the negotiation publicly. Lampert, who steered the company into Chapter 11 bankruptcy protection in October, is aiming to keep open roughly 400 stores and preserve tens of thousands of jobs. But how long Sears can survive under the 56-year-old billionaire, who has tried and failed to turn around the company many times before, remains an open question.