Why do messages appear on Lock Screen but not in the Messages app on iPhone?

“That's not correct definitely saw 2 telephone # & one which said ‘thank you’”

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Messages Not Showing in Lock Screen:

A. Close All Apps:

These Apps may be open. So, save what need be, and then close all apps. Hold you finger down as you swipe up form the bottom-left corner of your screen. Then, close all of these open apps, by sweeping up quickly for all apps.

B. Perform a Force Restart:

Try Force Restarting your iPhone. Save any information that need be. Then perform the restart. See if you can then see the results. Go Here: Force Restart iPhone - Apple Support

"Why do messages appear on Lock Screen but not in the Messages app on iPhone?: When turning my phone on msgs appear on the Lock Screen but when going to msgs they have disappeared"

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Messages Only Appearing ing Lock Screen:

Seems you are seeing notifications; not messages.