I've been struggling with the Firefox extension being severely broken for a few weeks, though I'm not sure if the behavior I am seeing is the same as what I have seen others describe. When clicking the Lastpass icon, only a tiny, empty popup would show, then all web pages would be unable to load until I disabled the extension. Well, I get the impression that Lastpass is intercepting the page while it loads to inspect it and modify the form fields, but is hanging on some request which prevents the page load from completing.
I do not run private browsing all the time, so I the workaround posted in the pinned support post
did not apply to me. However, I found another workaround that is viable for me until this has been properly fixed - from the Firefox addons page, click the Lastpass extension, scroll all the way to the bottom, and change the "Run in Private Windows" option from "Allow" to "Don't allow". It seems that passwords could still be copied from a non-private session into a private one if needed this way, though it is not ideal.