I don't think it works with Do Not Disturb (or at least I don't seem to get it). It only works for me when going in the Clock app > Bedtime and there turning Bedtime on. The lock screen will go black, Do Not Disturb will be automatically turned on and when the alarm goes off the good morning message will show on the lock screen. I also think that if you set a Schedule in Settings app > Do Not Disturb it will work too, just not when you regularly turn on Do Not Disturb.