One year after Lehman Brothers Holdings Inc. collapsed, the law firms that relied on it for significant billables are still adjusting to a new marketplace with one fewer player.

For some of the dozens of firms that served as Lehman’s outside counsel, the work goes on in bankruptcy court. Yet in the past year, law firms have been chasing their old contacts at Lehman who have scattered to other financial institutions. The competition is heating up as Lehman’s former firms vie for work performed by other banks’ long-time outside counsel.