There are plenty of feed readers on Android, but how many of them slap some news on your lock screen? Not many, I'd imagine. Corgi is an app that plugs into Feedly to pull in news and display it on the lock screen. Android lock screen replacements are never ideal, but Corgi seems to do a rather good job.
Corgi doesn't have much of an interface outside the lock screen UI. There are a few settings to add and remove sources, but it seems to just grab all your feeds even if you have categories set up. Some more refinement might be nice. At any rate, you unlock the phone, a story appears, and you can swipe to view (up), advance (right), or unlock (left). The animations in Corgi are slick and it's a cool idea, but the overuse of floating action buttons is confusing. Why is there a camera shortcut in the FAB? Why is it in the middle of some screens? I don't get it.
The app recommends you turn off the native lock screen and use Corgi, which has a pattern lock of sorts. It's not the same as having the actual system lock screen enabled, but it seems reliable. I'm not saying you necessarily should do this, but you can. The developers promise notifications and more options will be added in a future update.