While you’re probably aware that Apple added lyrics support to Apple Music in iOS 10, what may be less obvious is that you can also view lyrics on your fourth-generation Apple TV, using tvOS 10. Once you’re playing a track, touch (not press) the Siri Remote touchpad from the Now Playing screen and you’ll get the same detail view as before, but if the song has lyrics associated with it, a second button appears at the top of the screen that can be used to bring up the lyrics for the current track.
Not every song in Apple’s Music catalog has lyrics yet. If you’re listening to a song that lacks listed lyrics, you can still add lyrics manually via iTunes on your Mac or PC if you wish. These should sync via iCloud Music Library and be available on your iOS devices and Apple TV.