It's jointly owned by Naver and Softbank. A few months ago, there was a public outcry in Korea when the Japanese government threatened to twist Naver's arm to give up its share of Line, and South Korea's inexplicably pro-Japanese government stayed mum. With both governments enjoying abysmal public support, I have no idea how it will eventually be settled.
Why wouldn't Koreans care? We're talking about 50% ownership of a messaging platform that's de facto standard in multiple Asian countries. Imagine the UK government trying to force Google to sell DeepMind.