Apple Music doesn't (yet?) integrate lyrics, but if that's something you care about, there's a workaround you can use right now: a widget called Musixmatch. Federico Viticci noticed the functionality and wrote about it on MacStories:

I was listening to some playlists on Apple Music today and, to my surprise, the widget is already compatible with any song streamed from the service without an update required.

You can get Musixmatch on the App Store, and you can read more about how else Ticci uses it on MacStories.