I had the same problem ie Music player stayed on after LED case was closed. What you need to do is simply close the app via the bottom left button (close app) button and the LED will no longer show the music tab, just the clock.
I think I may have found an easy fix. I have this problem when using the Samsung music app. I've noticed that if I first pause the song I'm listening to and then close the app, the music controls get stuck on the Led View Cover. But if I close it while the song is still playing, the music controls close too. It works after it's already stuck as well. Just press play, close while the song is playing, and the music controls disappear. I haven't tried it with other apps.
Works with Samsung music but not for Spotify
Just purchased the Samsung LED cover for my new S10+, and Spotify is hangoing onto the LED cover alerts, 12/08/2019.
The only way I can see, is to remove the phone from the cover...very impractical and fustrating.
Just got the software update which seems to have fixed the issue.
A month and a half of pure frustration. Lovely. Really unimpressed with this, honestly, but at least it's better now.