If you added lyrics yourself to the songs, I can't explain why they are not visible. If you did not enter lyrics but see them in the music app, then the explanation is clear: the music app can access a lyrics database to show lyrics for songs that basically do not contain embedded lyrics. These lyrics can not be exported due to copyright reasons.
So if you added lyrics yourself, try the following workaround: On your computer, drag and drop the songs to an iCloud folder and import from there.