Cannot project Apple Music lyrics from iPhone to smart TV

What I want to do is project the lyrics of the song playing on my phone to my smart TV. I can do this with the Spotify app on the TV and my iPhone. I have tried to do the same with the Apple Music app and cannot make it happen. I can get lyrics that the TV app is playing but there doesn’t seem to be a way to ‘share’ the song on my phone to the app so I can share the phone’s song lyrics.

Using AirPlay will not share the lyrics either so that doesn’t work.

The reason to do this is because I have a JBL Party Box which is just Bluetooth speakers and included mics. But I want to push the lyrics to a bigger screen than an iPhone or iPad.