I don't know if you've done this yet. Go to Settings >Device>Sounds and Notifications. At bottom of screen there is a Notification section. This gives you options for displaying notifications on your lock screen. You can set notifications from any app. Lots of ways to customize.
Having said that, I don't see any weather app at all on my tablet. Also, I use Nova Prime launcher and got rid of the 2 news pages on my home screen. Weather may have been built into them and had an option to display weather on lock screen.
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