Artwork
If it's not intended for the app store, you could definitely use the artwork thing. Since you don't need to comply with the iOS guidelines, just warn your users that the lockscreen buttons won't work if you try using them. This link and this one should help.
Using the iOS 7 background fetch can help you manage messages display, as long as the app has already been opened once. To know if the app is opened, you can send ping to your server saving the current app state every X minutes. If the server doesn't receive an update, it will just guess that the app is not running, he'll send emails or push notifications to the user until he does so.
Issues:
- If the user opens an app like Music or any other that can become a responder, it will override your message.
- You can only display a message if the app is opened at least once.
Remote notifications
It could be a good option since a notification can stay on the lockscreen as long as the user or you doesn't clear the notification center (you have to set it). And you can remotely display any message without the app being launched.
Issues:
- You have no way of knowing if he cleared the notification. An idea would be to send them an email if notifications have been disabled.
- Users can just disable notifications.
Lockscreen image
You won't be able to change the device lockscreen image without a jailbroken device.
I'd go with the first one, if it's a client requirement it seems like a reliable one. It all depends on how much control they have on the devices.