The latest from Ken Auletta at The New Yorker, who, citing "extremely well-informed sources at the paper," reports:

Abramson was, essentially, fired for cause, for lying to Sulzberger.

In the New York Times, David Carr recounts a similar-ish series of events, though he focuses on an alleged (and related) misleading of someone other than Sulzberger, and the word "lie" is not present.

However: Both Carr and Auletta suggest that if a newspaper is indeed being run by a dishonest editor, in the end it's the publisher's fault.

Carr: "The current mayhem aside, Mr. Sulzberger’s real failing has been picking two editors who ended up not being right for the job." Auletta: "Sulzberger has been, to say the least, an imperfect steward of the paper."