Same problem here. It started on my Pixel 3 and now I've upgraded to a Pixel 4a 5g I see exactly the same issue. It has persisted across Android upgrades. I can authenticate using my fingerprint within the LastPass app (and in other apps) but the LastPass pop-up doesn't work.
This is compounded by my frustration with the failure to properly implement FIDO/U2F security. I'm going to investigate the competition, starting with either Bitwarden or 1Password. I've heard good things about both of them, but I'm not about to jump ship in a hurry in case they have their own issues.
(FWIW, I'm the admin of a LastPass Enterprise account and have recommended it to multiple friends and family. If I move, then over time LastPass are likely to lose dozens of licenses - and if I manage to persuade my employer to roll out password managers globally, thousands of licenses.)
My Premium account expires on January 29, 2022. I'll be onto 1Password by then. I suspect LastPass QA hasn't tried very hard to reproduce this problem so they don't take it seriously. Too bad. It's a fatal flaw on mobile.
Just wanted to say that they finally almost fixed the issue. Now when trying to fingerprint unlock for autofill, instead of an overlay, a lastpass window opens up and it does unlock successfully.
There is still a bug though, if you have an account protected by password (not lastpass, one of the saved accounts) and try to autofill in a new app, it will ask to unlock twice, first one for lastpass and second for the account, but at the end nothing will happen. To fix this, remove the password protection from the account, try to autofill, it will prompt a message to confirm the autofill in this app and then it will work. You can enable the password protection back after this. The issue here is that confirm prompt not showing up when the password protection is enabled.