In the US, lawyers and accountants had received $917 billion by July, with the $1 billion mark expected to be passed during this month, reports the Financial Times.
Legal costs for the European arm of the business - which are being dealt with in London â are believed to be close to reaching $900 million.
PricewaterhouseCoopers is dealing with the European administration of the Lehman Brothers estate and still has more than 300 people employed on the task.
In the US, around 1,000 professionals are working to clear up issues with the bank's accounts.
But the legal costs of the operation are still tiny in comparison with the size of Lehman Brothers' balance sheet at the time of its failure, which stood at $691 billion.
Earlier this month, Bob Bernanke, the chairman of the Federal Reserve, said that the dire state of Lehman's finances at the time of its collapse meant a government bailout would have been unjustifiable.
By Gary Cooper