Richard Fuld's plan to keep Lehman Brothers Holdings Inc afloat depends on whether the chief executive officer can sell a business that he'd rather keep to a buyer who may not be able to pay for it.

Lehman told investors on Wednesday it will auction off a 55 percent stake in its asset-management unit, which oversees $277 billion, including funds run by Neuberger & Berman LLC. Private- equity firms KKR & Co LP, Bain Capital LLC and Hellman & Friedman LLC may make bids valuing the unit at about $5 billion, according to two people familiar with the negotiations.

Losses of $6.7 billion in the past two quarters and an almost 90 percent drop in Lehman's stock since the start of the year forced Fuld to put the division up for sale after prices for fund companies dropped to the lowest since 2002. The lack of financing for leveraged buyouts will make it harder for the New York-based securities firm to pull off a deal.