If you want your iPhone's notifications in Notification Center to mirror notifications on your Lock Screen, you can at last do so as of iOS 9, thanks to a handy preference in the Settings app.

  1. Open the Settings app.
  2. Tap Notifications.
  3. Select Sort Order.

  4. Tap Recent, then tap the back button.
  5. Turn off Group By App.

Now, when you pull down Notification Center, you'll see your notifications as organized by time, rather than by specific app.