When I go to the lock screen settings none of my weather app appear in the quick status menu. I'm using a Lumia 925 with the black update. Is there anyway to add them manually?
The apps themselves must support such feature. Then you will be able to pick those apps there. Nothing you can do to add them as it requires extra code from the app.
While virtually all the weather apps can function as your lock screen, I don't believe any of them have notifications the way things such as email or messaging, nor do I believe any of them can give a detailed status like the calendar. Perhaps you may want to look at something like Awesome Lock?
There is such an app... But don't remember the name... Danial wrote an article about how u can use glance feature to stay updated with temp... But you have to find that article...