Hello,
The song will need replaced with the versions from the Apple Music catalog.
See time-synced lyrics in Apple Music on your iPhone, iPod touch, or Android device - Apple Support
"If the Lyrics button is grayed out
If nothing happens when you tap Lyrics
, then either you’re playing a song that's not from the Apple Music catalog, or lyrics aren’t available for that song."
Add music to iPhone and listen offline - Apple Support
"Add music from Apple Music to your library
Do any of the following:
- Touch and hold a song, album, playlist, or video, then tap Add to Library.
- When viewing the contents of an album or playlist, tap
near the top of the screen to add the album or playlist, or tap
, then tap Add to Library to add individual songs. - On the Now Playing screen, tap
, then tap Add to Library.
To delete music from the library, touch and hold the song, album, playlist, or music video, then tap Delete from Library.
Music you add to iPhone is also added to other devices if you’re signed in to the iTunes Store and App Store using the same Apple ID and have Sync Library turned on (go to Settings
> Music, then turn on Sync Library)."
I hope this helps.