Defunct brokerage Lehman Brothers Inc, which hasn't paid hedge funds after four years in liquidation, is nearer to making them whole after reaching a "critical milestone" in settling a $38 billion dispute with an affiliate, the trustee said.

Brokerage trustee James Giddens, who is facing payment demands by New York hedge fund Elliott Management Corp, said the brokerage approved a $7.5 billion customer claim by Lehman Brothers International Europe, plus income of $600 million, with another approved claim of $500 million by the affiliate. The brokerage will get a general claim against LBIE of $4 billion, he said in a statement on Friday.

"This is a critical milestone for customers because, if approved by the court, the agreement sets the stage for distributions that will provide for 100 percent recovery of customer property," he said. "The agreement resolves tens of billions in claims from LBI's largest single customer claimant and will allow for customer and creditor distributions much sooner than if LBIE's claims involving hundreds of thousands of transactions were litigated."