It's a convoluted set of details, but from what I gathered (reading quickly), it comes down to a he-said, she-said between her and Baquet, her replacement, and the publisher is going with Baquet. The Times was trying to recruit Janine Gibson from the Guardian, and according to Baquet, when he was having lunch with Gibson, she informed him that her rank would be the same as his.
Baquet claims this was humiliating news to him, and Abramson claims that she had worked all of this out with him already.
@3: and there seems to be independent corroboration that it was Baquet. Maybe he misunderstood what he was being told, but the other party involved (Gibson) seems to have understood what Abramson was going to do.
Just going by the New Yorker article, this "lying" sounds like a pretext for the firing, not the actual cause.
@7 Of course it's a pretext. This is the executive editor, not a new kid in the mail room. They are trying to craft an alternative narrative to the idea that she was fired for demanding equal pay. They need something to present as defense at the lawsuit.
Baquet claims this was humiliating news to him, and Abramson claims that she had worked all of this out with him already.
Just going by the New Yorker article, this "lying" sounds like a pretext for the firing, not the actual cause.