Sears Holdings Corp. controlling shareholder Edward Lampert spent years keeping the retailer out of bankruptcy court. Now a $300 million lifeline and a speedy chapter 11 sale may be his best chance at keeping control of its remains.

Early Monday, Sears filed for bankruptcy protection after years of struggle and relentless losses. Sears said in court papers it faces catastrophic consequences if it can’t repair its supply chain and keep merchandise flowing to the company’s stores and warehouses.

Some...