I exchanged a few messages with lead developer at Last Pass a few days ago.
They've put Aqua on their blacklist -- i.e. won't try to integrate with their new "apps not just web browser" password filling.
You will need to "update your vault" (hope I got the wording right) to pull in this new setting.
As to the cause and whose bug it is --
The developer said they were seeing this issue in several apps, and in each of those cases, it turned out to be a bug in the app, not in LastPass.
He even told what the bug was -- "the" because according to him, it was the same bug in all of them.
Well, if Aqua had a bug like this, it would be crashing when viewing messages. So that theory is wrong.
Other than that, he said they use the built-in Android accessibility service to fill passwords, that it's part of system code, also that system code behind WebView received a major update in 4.4...
To summarize: his theory about something being wrong in Aqua is false, he has no better solution, and if this is all caused by something in system code, he has no solution either.