According to the developer Bardi, his app Appy Weather is about to get an update by the end of this week which will bring lock screen support.
He noted the changelog is relatively short, with a few bug fixes only, but the lock screen support is widely adjustable and very flexible.
The update is not live yet but we expect it to come online very soon. We will update this article when it is available. In the meantime you can get Appy Weather here.