Bank of America
The bank said in papers filed on Wednesday it would post a $660 million bond and asked the court to stay the enforcement of the ruling.
A hearing on the issue is set for January 19, according to court documents.
In November, Judge James Peck ruled that Bank of America violated federal law when it brazenly seized $500 million of Lehman's deposits, taking advantage of Lehman's weakened condition in the summer of 2008.
The judge later ruled the bank must also pay interest, which brought the total to about $595 million.
The decision was a victory for Lehman as it tries to repay creditors still owed hundreds of billions of dollars following its September 15, 2008, bankruptcy.
A Lehman Brothers spokeswoman did not immediately return a call for comment.
The case is In re: Bank of America NA vs Lehman Brothers Holdings Inc et al, U.S. Bankruptcy Court, Southern District of New York, No. 08-ap-01753.
The main bankruptcy case is In re: Lehman Brothers Holdings Inc in the same court, 08-13555.
(Reporting by Tom Hals; additional reporting by Santosh Nadgir in Bangalore, editing by Dave Zimmerman)