Mr. Leung was indeed allowed to serve his term but not allowed to re-run (which was his ambition). The Umbrella movement ended his political career and he served out his term as a lame duck. No matter how you spin this, he basically left the political scene with his tail between his legs. Carrie Lam is similarly politically dead. Unlike Leung, I expect they won't keep her around as the protests are increasingly about her specifically. Neither Lam nor Leung had any say in this matter; it's all about what Bejing allows to happen. Clearly their handling of the Umbrella movement just set them up for what's happening now, which in terms of scale and popular support is a problem for the current leadership because their ability to keep the lid on this domestically is not infinite and they need the two party system to be a success to keep a grip on Taiwan, which is another thing they seem to not have under control lately.

So, I'm predicting they will seek to remove the problem a bit sooner and ms. Lam seems like she's expendable, politically dead anyway, and a big part of their problem.