Live Activities are usually added automatically to the Lock Screen, but unfortunately we have seen that the background push notifications that are supposed to launch Live Activities have a few system limitations:
The max number of Live Activities that Forza is allowed to display may already be reached. This number is changing depending on the system conditions, we have seen everything from 2 to 15.
If the device is on low power mode, Live Activities almost never start automatically.
If Forza hasn't been launched relatively recently, the system devices is low priority and may not launch the Live Activity.
If the app is not running in the background, the Live Activity has lower chances of being launched.
We hope Apple addresses these issues soon or at least offer a way to workaround them in future iOS versions.