It's a little hard for me to test right now, because I currently can't get someone to send me a text.
Just to be sure -- go to Settings>Security>More Security & Privacy>Notifications on Lock Screen. Is that set to "Show all notification content" or "Show sensitive content only when unlocked"? If the latter, that might explain your situation, since the lockscreen is showing that your phone is locked (since you see the fingerprint there).
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