This is actually happening on my 5C and my iPad air but sometimes I get one message notification on the lock screen sitting on top of another one and then when you swipe it to open it you can see the one underneath anyone else?
You can still set up as new. Go to settings, general, reset, erase all content and settings.
This will return your phone to standard and hopefully solve your problem.
There's no harm in restoring a backup and seeing if the problem has persisted or maybe just a fresh start with a restored backup will solve it.
If the problem remains after the restored backup you'll have to repeat the steps but set up as new and see if that solves the problem.
Good luck
Update correction, I'm still getting the notifications piling on top of each other and not spread out on the lock screen. Doesn't happen all the time maybe once a day.
Strange. I haven't seen that. How often do you see that? Is it happening on all notification or just iMessages?