Have you checked any of the settings for this? We don't know what device you have but the devices I'm familiar with usually have lock screen settings, usually find this one in the security section, whether to show notifications on the lock screen or not and how detailed or generic those notifications are. There are also settings in Snap. The only one I can find that sounds like it might be of some help is Wake Screen, which sounds like it would wake a sleeping device, which would obviously be on the lock screen, to display a message. There are also Notification settings on the app page in Settings>Applications>SnapChat, notifications.