MusixMatch is the most popular platform for searching and sharing music lyrics. According to Wikipedia, it is the largest lyrics platform in the world with a total of 60 million users, 14 million lyrics and 30 employees since its establishment in 2010.
MusixMatch hasn’t officially announced a desktop app for Linux but there actually is an available client you can use. It runs in its own window with the lyrics set to float on top by default. The Window is responsive and features mouse-over play/pause controls, alongside links to edit or synchronize lyrics.