For good or for ill, I'm not a lawyer. I'm just someone who's miffed at the way the copyright interests keep squeezing and squeezing, trying to turn the law to their favor every way they can.
I'm pretty sure that not-for-profit status has no effect on whether you can publish lyrics. It may matter to whether and how the Mudcat comes under other areas of copyright (e.g. the radio program). The Lyrics in the DT, though, must all be in the public domain or copyright-cleared. This probably is the vast majority, isn't it? So even if we have to cull the DT of uncleared copyrights, we'll still have a pretty big database ?
As I mentioned earlier, the occasional posting of copyrighted lyrics to this forum (as opposed to the DT) OUGHT to be a fair use. There's nothing systematic about it (as was the case with intabulations posted to the OLGA). It's just once in a while, it isn't the main purpose of the forum, no one can find them through a web search (at least I don't think so), and most threads vanish after a few weeks into the forum archive, their existence known only to a few regulars. But to be safe, we may have to cull those posts from the forum archive. We can substitute a message like "Lyric withdrawn due to threats from _____ (substitute some appropriate epithet or designation). See the following book" followed by a citation to a book where the lyrics can be found, or by a hyperlink to a well-heeled lyric server that can afford clearance.
This demand from the NMPA wouldn't be so annoying if the duration of copyright were more reasonable. (I hope y'all don't mind. I can't resist going on about one of my pet peeves.) I hope our Australian, Canadian, Japanese, Swiss, and other friends encourage their lawmakers to hold the line at life plus 50 years (which is still too long), at least while the recent U.S. extension is being challenged in court. Maybe the recent orgy of copyright extensions can be reversed, or maybe, at least, we can be well enough organized to have a fighting chance of preventing the next extension when the entertainment industry asks for one in about 15 years.
Disclaimer: as usual on the web, this post is private opinion, nothing in this post is legal advice, and nothing in this post establishes a lawyer-client relationship. (I'm not even a lawyer!)