is it possible to display something on the Windows Phone Lock Screen triggered by a push notification?
According to this graphic, I understand that's it's only possible via local notifications, or am I getting something wrong? I would like my app to make notifications on the lock screen whenever something important happens, which is triggered via remote push notifications from my server - is this possible?
Actually, it is possible. The lock screen just reflects the information of the main pinned tile of your app. So, if you update the tile, for example sending a tile push notification, the lock screen will be updated too.
Note, that you cannot programatically set your app to show notifications in lock screen. User has to manually select it.
You may find this post useful:
http://www.silverlightshow.net/items/Windows-Phone-8-Live-Tiles-and-Lock-Screen.aspx