Thank you for reaching out to us to address your concerns, Have you tried the troubleshooting steps for Controlling what notifications appears on your lock screen?
You can locate those steps here: http://www.samsung.com/us/support/answer/ANS00062636/
I see a lot of posts about not getting notifications on the S20, especially on the lock screen. Took me some trial and error but I eventually figured it out. Turns out it's a small setting the way the S20 comes out of the box.
First let's look at the root of the problem. Go into settings, click on notifications then click on messages. From there click on general notifications and take a look at the lock screen setting. Notice how it defaults to 'Do not show notifications' with no way to change it (at least not from here).
Solution is simple, go back to main settings, and click on lock screen. Notice the notification setting has defaulted to OFF for some strange reason. At least from this menu you can just click on it to turn it on.
You can confirm the problem is fixed by going back to the locked screen and have someone send you a text or email. All is right in the world again. :-)