So I've had this issue on and off for years, across 2 iPads, but just worked around it by opening the app directly and copy/pasting manually.
I spoke to support 2022-06-11 and they advised it's some kind of issue with the external keyboard. I was pretty sure it happened both with and without the magic keyboard attached in the past, but today on the newest (5.12.0) version of Lastpass I actually found that auto-fill stays open as long as I need it to, as long as I'm not attached to the external keyboard.
TLDR: Seems to be "fixed" by temporarily removing the external keyboard.
I've run every test they've asked me to do for almost a year now and still have the issue. Over and over they've said that the latest update will fix it but it never does.
Just the iPad; the iPhone continues to be fine. No external keyboard.
Can’t believe this issue is still happening. It’s completely frustrating and a obviously a bug. Lastpass, you have pretty much ruined most of our lives this year with horrible UX issues on the iPad, disgraceful security breaches of our vault data and the new Chrome pluging UX is atrocious and runs rampant on auto-saves…how about owning up to this bug that has been around for YEARS on the iPad and fixing it!!!!