I'm pretty sure very, very few bands/artists in the Korean pop industry write/compose their own songs. I think C.N.Blue might? I heard Yonghwa does lyrics at least.
But most artists/bands just buy songs from someone and aren't involved in the actual creation of the song...
That's why you have something like the Hyori/Bauhnaus controversy.
Are you talking about this video? I looked up Lucifer and 4minute and this was the only thing that came up...
That's just the song put to the MV...