What the article in the OP shows is that this attack may indeed have been spontaneous and motivated by the video.
The administration has been proven wrong about only one thing so far . . . that there was a protest. They have not been proven wrong that the incident was spontaneous in nature or motivated by the video. And as the article indicates, there is solid evidence indicating that those theories are correct.
So they were wrong about the protest. But did they lie? There is no proof that the administration knew there wasn't a protest during the time it asserted that there was. The emails don't prove the incident didn't begin as a protest. Reports from the scene initially indicated there was a protest. The CIA briefings to the president said there was a protest. So there is really zero evidence whatsoever that this is some kind of "cover up."