HOFFMAN ESTATES, ILL. — Former Sears CEO Edward Lampert has won a bankruptcy auction for Sears Holdings Corp., according to The Wall Street Journal and other media reports. The billionaire hedge-fund manager upped his offer to about $5.3 billion from $4.4 billion. The offer, which will keep roughly 400 stores open, beat out a bid to close all the stores and sell the inventory. The plan must still be approved by the bankruptcy judge at a sale hearing set for Friday, Feb. 1. Last week, REBusinessOnline reported on Sears’ temporary deal to avoid liquidation.