There's a difference between pop icon and icon. If you're an icon for music in general, you've made it so big that you're well-known by everybody, and everybody listens to you or has listened to you somewhere along the line. The Rolling Stones, Bob Marley, Elvis, etc. Lady GaGa is not a musical icon, she is a current pop icon. Britney Spears was a current pop icon, now she doesn't release music and if she did nobody would even care. If she became a jazz singer, she'd have some serious competition though, because Norah Jones owns that category.
Now if she can keep her fame for many years with album after album of hits, then it's fair to call her an icon.