I am having the exact same issues. I do get the accept button, I click it to accept and then I also see the blank window.
Other extensions that are also in use are uBlock Origin and Privacy Badger too.
Until this gets fixed, I've found a workaround that seems usable.
On a blank tab in a private window, click on the LastPass icon. If it is the first time you'll need to click Accept. When you get the blank window, right click in the blank area. Go to This Frame and then Show Only This Frame. The tab will become the LastPass box, and you'll be able to use it like normal.
In the same boat. Also have uBlock Origin and Privacy Badger (et al.) extensions, but the defect still occurs even when I disable them (one, the other, or both) in private windows.
Frames comments above check out too. I too can "Show Only This Frame" and get a functional LP private tab. It doesn't really add any value, though, since it's not attached to (operating on) any active/current tab and so I might as well just use the drop-down version from a non-private window.