Must there be notification alerts for anything to appear on lock screen? I disabled Instagram from posting a notification alert ( banner or alert ). 
However any posted item or notification do not show in the lock screen or notification center. 

Prior to ios7 this causes no problem, as comments/notifications from such an app show up in the lock screen or notification center, but is this feature disabled now ?
How did you disable the notification alerts?

You should have three different settings in the notification settings:


Alert Style: if you set this to none, you will not see any banners or alerts when you have your phone unlocked.
Show in Notification Center: you should keep this on
Show on Lock Screen: and this one on


Those settings should be independent to each other I believe.