Weather app notifications are not appearing on the lock screen.
I went to PC Settings and added the Weather app to the list of lock screen apps in the Personalize pane, but this had no effect. The lock screen looks the same as it did before.

There are two settings for lock screen apps in the Personalize section of PC Settings.

The first setting allows you to select which apps you would like to “run in the background and show quick status and notifications, even when your screen is locked”. If you add the Weather app to this list, the Weather app will only display a notification if your chosen default city has an alert, such as a Severe Weather Alert or other such warning issued by NOAA. If there is currently no such alert, you will not see anything from the Weather app on the lock screen.

The second setting is to “Choose an app to display detailed status”. Only one app can be specified here. If you select the Weather app here, then you will see the current weather for your chosen city next to the time on the lock screen.

Here are the detailed steps for enabling Weather app notifications for the lock screen:

Step 1: Turn on notifications in PC Settings. (This should be on by default.)

1. Open the Settings Charm.
2. Tap or click Change PC settings.
3. Tap or click Notifications.
4. Slide the Show app notifications and Show app notifications on the lock screen switches to On.

Step 2: Add the Weather app to lock screen notifications
1. Open the Settings charm.
2. Tap or click Change PC settings.
3. Tap or click Personalize.
4. In the right pane, with the Lock screen tab selected, under Choose apps to run in the background… tap or click one of the “plus” symbols and select Weather.
5. Then under Choose an app to display detailed status, tap or click the icon beneath it and select Weather.