It is supposed to work like this:
But it looks like the artist lessons are not always available for downloading again.
Do you still have a TimeMachine backup from the time you bought the lesson? Then you can restore it from the backup. You need to restore the following file in your system library:
/Library/Application Support/GarageBand/Learn to Play/Artist Lessons/
Open the folder "Library" at the top level of your system drive, then "Application Support", then "GarageBand", then "Learn to Play".
With this folder open and selected enter Time MAchine and go back in time, until you find Sting and restore it.