The stack trace shows it's failing on writing to wherever it's intending to log the error. Here's the relevant chunk of code https://stash.openntf.org/projects/OPENLOG/repos/xpages-openlog-logger/browse/OpenLogOSGi/com.paulwithers.openLog/src/com/paulwithers/openLog/OpenLogItem.java#1202.
If you've got the xsp property to log to email, you'll see it's using signer access to write to mail.box (or if there are multiple mail.boxes on the Domino server, it just picks one of them, even if none are actually called mail.box).
Otherwise it's writing to the database defined in the xsp property or, if you don't have one set, OpenLog.nsf. You'll see it's checking for database is null and it's not generating that error. So it looks like it can't write to that database for some reason.
The most likely cause is that the user triggering the error doesn't have at least depositor access to the OpenLog database.
If they have access, it would also be useful to check whether Domino runs a consistency check on the OpenLog database on startup. If it does, there may also have been a problem that prevented it writing to the database when logging the error. I have seen OpenLog databases get quite large, which is why I now use the xsp property to set an expireDate and add an archiving setting on the database to ensure logs are only kept for e.g. 90 days. Another possible cause, depending on timing, is that another process is locking the OpenLog database, e.g. backups.
Hopefully that gives you a better understanding of what's happening at that point and potential causes. It would be interesting to know what you find out. Maybe the code can catch this error and write to the console instead, although that would not be able to log as much as it logs to OpenLog.