I had the same issue with native Mail app not notifying on lock screen, had 3 advisors 2 at Senior team level to diagnose the issue and not working. I dont use icloud email but the yahoo gmail and POP mails.
I have tried force restarting, deleting and reinstall Mail app and even reset iphone to a new iphone and downloading all apps from icloud! Doesnt wotk! I can get lock screen notifications from other apps even the third party apps but not from the native Mail app.
Its annoying when you hace to login to see the mails.
I think it is a bug with the iOS and when i checked my wife's iphone seems it is also affecting her iphone.
I actually scheduled a visit to store and to get the technician to check my iphone probably the software or configurations etc. Not sure if they can get it done.
Not sure if they can make things work.