Trustee James Giddens, who also is liquidating the MF Global Inc. broker-dealer, asked a judge to approve the distribution yesterday, more than three years after the Lehman parent filed the biggest bankruptcy in U.S. history. He didn’t say how much money customers can expect, only that his goal was to make “a significant” payment. Large payouts must await resolution of remaining disputes over claims, he said.

“The trustee would like to be in a position to proceed with interim distributions to customers in early 2012, with reserves as appropriate for disputed claims,” Giddens said in a court filing yesterday. “Disputes involving the largest dollar values will have to be resolved before large distributions of customer property can proceed.”

By law, Giddens must share the assets equally among customers. He has gathered $23.7 billion to pay customers from settlements, litigation and negotiations with banks and other business partners, according to records in U.S. Bankruptcy Court in Manhattan. He is holding $3 billion of the total in reserve for a continuing court fight with Barclays Plc, which in 2008 bought North American businesses of the brokerage’s parent, Lehman Brothers Holdings Inc.

Billions of dollars also are at stake in Giddens’s disputes with Lehman Brothers Holdings, its London affiliate, and counterparties to mortgage contracts and repurchase transactions, according to the filing.

The brokerage has spent $642 million on its liquidation, with most of the money going for professional and consulting fees, Giddens disclosed in October. The trustee and his law firm, Hughes Hubbard & Reed LLP, have earned about $169 million in fees since September 2008.

Lehman Brothers Inc.’s remaining customers include hedge funds and other institutions. Soon after the bankruptcy, 110,000 customer accounts with assets of $92.3 billion were mostly absorbed by London-based Barclays and New York-based Neuberger Berman Holdings LLC.

The Lehman brokerage liquidation is Securities Investor Protection Corp. v. Lehman Brothers Inc., 08-01420, U.S. Bankruptcy Court, Southern District of New York (Manhattan) .