Hi, I am Dave, I will help you with this.
To avoid screen burn-in on that monitor, you cannot set a live wallpaper in the Windows 11 lock screen, you can set the lock screen to a slideshow of photos you have stored on your PC, or you can use one of the old animated screensavers, they should still work in Windows 11, they are accessible from Settings - Personalization - Lock Screen at the bottom.