Separately, a corporate law judge on Monday refused to throw out a lawsuit blaming Lewis and the board of directors for failing shareholders in its purchase of Merrill Lynch.
But Vice Chancellor Leo Strine said the case could be an "exceedingly difficult" one to prove against outside directors, which means all members of the board except Lewis, Dow Jones said.
Last Tuesday a team from Cuomo's office met with BofA's lawyers. Initially the bank resisted the attorney general's request to waive attorney-client privilege and turn over additional documents linked to Bank of America's purchase of Merrill last year.
But at the meeting the bank's lawyers said they were reconsidering the bank's stance, the source said.
According to the source, on Thursday the bank's lawyers told the attorney general they would present his request for additional information to the board and that the board approved the request Friday.
Bank of America did not return calls seeking comment. Cuomo's office declined comment.
Cuomo has been investigating whether material information was withheld from shareholders prior to the Merrill deal being finalized. The questions center on what and when Bank of America executives knew about Merrill's mounting losses and the billions in bonuses paid to Merrill employees and why this information wasn't shared with investors.
Some BofA executives deposed by Cuomo said in withholding certain information about the deal, they acted on advice of counsel.
Citing attorney-client privilege the bank declined to hand over records the attorney general's office believes are critical in determining whether the executives did indeed act on counsel's advice, or did so on their own.
The source says its likely executives, including CEO Ken Lewis and Chief Financial Officer Joe Price will be deposed again, once the attorney general's team has a chance to review the documents.