Edward S. Lampert, struggling to stem heavy losses at Sears Holdings, is facing an exodus of money from his hedge fund.

Lampert's hedge fund is returning billions to clients of Goldman Sachs, who had invested with ESL Investments in 2007, according to people with knowledge of the matter. Under that deal, Goldman's clients, such as corporate pension plans, put roughly $3.5 billion with Lampert, and they have asked for it back.