Mail not showing up on lock screen

Here is my scenario.

When waking up in morning noticed that emails received during the night do not appear on lock screen. When going in to the iPhone I swiped down to see notification center and new emails were not there. However once I opened mail, and it received emails, I was then able to see them in the notification center. Should it not show the emails on the lock screen without opening mail program?

BTW, I checked settings for Mail notification center and the following options were set.

Notification Center: ON

Alert Style: Banner

Badge App Icon: ON

Show Preview: ON

View in Lock Screen: ON

Thanks and I look forward to your reply.

...Bruce