April 2018 and this is still an unresolved issue for many people. My husband’s iPhone X is on the latest iOS and his lock screen has been doing the same thing with the Music notification.
My iPhone 7, also on the latest iOS, has never had this issue.
My husband has followed every suggestion to remove the Music notification from his lock screen, with the exception of erasing his iPhone.
The first troubleshooting steps always include turning off Notifications > Music > Show on Lockscreen. I believe this step doesn’t address a thing, because I have, and have always had, EVERY Music Notification turned ON, yet my iPhone lock screen has never had the Music notification.
I often leave iTunes open with a song paused on my phone, unlike my husband who only listens to Pandora. Even under these circumstances, my iPhone lock screen does NOT show Music.
This issue will only be resolved by the Apple engineers in a software update.