On Apple Watch, there is no LifeSaver app and notifications on your Apple Watch will not affect your LifeSaver score. You can however, configure the watch through its settings to not display “Keep your eyes on the road” banner from LifeSaver.
Here’s the link on Apple Watch and how to set notifications on or off for 3rd party apps:
Choose which notifications you get
You can customize the notifications for each app that you use with your Apple Watch. By default, your Apple Watch notifications mirror your iPhone settings. For example, if you set your iPhone Mail app to notify you only of VIP emails and your watch notifications mirror your iPhone, you’ll see only VIP email notifications on your Apple Watch.
For built-in apps, you can choose which notifications you get:
- Open the Apple Watch app on your iPhone.
- Tap the My Watch tab, then tap Notifications.
- Tap an app. If you want the app’s notification settings to mirror settings on your iPhone, tap Mirror my iPhone. If you want to choose certain types of notifications to get on just your Apple Watch, tap Custom.
For third-party apps, you can turn off notifications. Scroll down to the Mirror iPhone Alerts From section and turn off the setting next to the app.