Yeah, that's sad, I'm having the same issue. I have a lot of songs the database doesn't know and knows but don't have lyrics. On the first point, the website or the app doesn't let me add or simply sugest to put them in the database. There's also this situation where the database knows the song but don't have lyrics and even so the website or the app doesn't let me add them, by reasons like country block or by not giving me that option.
It's a very sad situation, cause I'm willing to contribute to the catalog with lyrics, translations, etc. , but I just get a big NOPE and there's no information or guides about this kind of issue.
@Wagner me too. I want to add a japanese lyric but the app just blocks.
I can understand the risks related to foreigners adding lyrics, but i don't think someone would add lyrics in a language that he knows. But a foreigner for example, would like to know the meaning of the song he likes, so overall i think foreigners are likely to add more lyrics from that language than the native people.