Hey JACKRUBY,
It sounds like you have a concern with these horizontal lines appearing on your display.
Since you're still having trouble after resetting the NVRAM, see if the display still behaves in this way in safe mode: How to use safe mode on your Mac. After testing in safe mode, restart and test again.
If the issue occurs in safe mode, as well as after restarting normally, then try a test user account. Here's how to create a new user account for testing purposes: Set up users, guests, and groups on Mac. If it doesn't happen in the test user account, the issue could be caused by a third-party program or certain settings on the main user account.
Keep us updated!