FCP 11.1.1 appears to work OK and doesn't update library.

No new features, just bug fixes, so no, update is not necessary, there's nothing to update once it's a version 11.1n Library.

Thank you, Ian. I concur. Just a quick clarification to point out that when you say it doesn’t require updating libraries that applies to libraries created in version 11.1, or some other 11.* version. I know you know that, but others might not.