In this scenario, the app will update and clear badge and tile notifications on the lock screen.

Lock screen apps can display up-to-date information through badge notifications and tile updates. Badge notifications are limited to an integer or glyph that is displayed next to a monochrome badge associated with the app. The badge displayed on the lock screen is the same badge that is displayed on the app's Start tile. Tile updates are sent in the same manner as updates sent to the tile on the Start screen, but are limited to text only and must be wide templates. The most recent wide tile update for the app will be displayed on the lock screen. If an image-only template or the default tile is set, then nothing will appear for the app in the detailed status slot on the lock screen. Users must manually select which app may show tile notifications on the lock screen. Please see the "Tiles" and "Push and Periodic Notifications" samples for more information on how an app can display update tile notifications. Send badge notification Clear badge notification

Send tile notification Clear tile notification

Above, the NotificationsExtensions library is used to create notifications. You can also create notifications with strings:
Send badge notification Send tile notification