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.
- Open the Settings app.
- Tap Notifications.
- Select Sort Order.
- Tap Recent, then tap the back button.
- 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.