I apologize in advance for posting this without thorough testing.
From my brief tests, the above field is not doing anything when set using:
mbApi.Library_SetFileTag(mbApi.NowPlaying_GetFileUrl(), MetaDataType.HasLyrics, "Test")
Is it read-only from the API side?
______________
The reason I'm even looking at it is because of:
I've looked and searched and can't find a way to access the "Mark as having no lyrics" option outside the Lyrics tab in the Tag Editor.
So this is all assuming "HasLyrics" has some relation to "Mark as having no lyrics".
If it doesn't, then the whole exercise is futile and there isn't a need to investigate the first half of this post.