It's driving me nuts seeing those notices each time I open my phone, leaving no room for the transient notifications and messages I've received.
Not possible, it seems. There is a thread on XDA about this: http://forum.xda-developers.com/google-nexus-5/help/hide-ongoing-notifications-lockscreen-t2938422
An app called Notific does the job beautifully. It has a pro version which allows you to select which apps you want to show notifications for. It has many more useful customisations too.