As I said above, I have seen this sort of issue before in the forum. I just can't remember the cause or solution. I can't find a good thread on it either.
If the files aren't read-only, check permissions on the NAS carefully. It could just be that MC no longer has write permission. Or the Windows doesn't, as MC uses Windows file functions, and as per your image, those are Windows File Transfer events. That is, the issue is happening outside MC control. But I'm not sure of that.
However, an upgrade to the firmware on a NAS has caused issues like this in the past. See
https://yabb.jriver.com/interact/index.php/topic,74707.msg506730.html#msg506730Have you made any recent firmware changes on the NAS, or allowed them to happen automatically?
Have you made any other changes to your NAS recently?
The other possibility is MC having problems with special characters such as "é" in file or path names. Some versions of MC had issues with special characters, or appeared to, particularly when they were stored on different file systems, which handled such characters differently. But only one of the examples in your image ha an accented character, so maybe that isn't it.
What exact version of MC are you running?
But first, I would just reboot the NAS and the MC PC, and maybe the router and all devices between the NAS and PC. That may do nothing, but it may clear whatever is going on.
Please also confirm that this doesn't happen if you make changes to any other tag that is written to the file. Perhaps add some comments to a file and see if the same thing occurs. If this only happens with the Lyrics lookup, maybe the file handling for files on a NAS hasn't been done correctly for just the Lyrics functionality. I know you said 'This only happens if I have the "lookup lyrics..." checked and to files that have no "lyrics"', but just to be sure.