Figure out notification settings

I can’t figure out how to set the applications notifications.

I get “off” that’s easy but “on” and “priority” I have trouble with.

For exemple: I have an application “phono” that tells you if your phone is in roaming or not. If I set it on “on” it doesn’t appear on the notification bar (internal application settings are on) and if I set it on “priority” I get notifications on the lock screen which is really annoying.

If it’s “priority” is it on the lock screen anyways or is there a way to change that?