You can set a wallpaper on both the home screen and lock screen of a supervised iOS device. As mentioned, the device will need to be supervised. Supervision can be implemented via Apple’s Device Enrollment Program (DEP for short), but DEP will require MDM to implement supervision, and with a device enrolled and supervised via MDM, you’ll need to use the MDM to set the wallpaper. You can also use Apple Configurator 2.
To use Apple Configurator 2 to set a wallpaper on a supervised iPhone or iPad, first save the image or images lo call on an iOS device. Once saved to the Apple Configurator machine, open Apple Configurator 2 and plug a device in.
Then right-click on the device, choose the Modify menu and then Wallpapers… from the Modify menu.
When prompted, use the Choose image… button to set the Lock Screen (the screen that is displayed when the device is locked) and the Home Screen (the background behind all your icons on each screen of the iPhone or iPad).
Once you have chosen the appropriate images, click on the Apply button.
You can also set lock screen text from Apple Configurator 2. To do so, use the “Custom Text…” button at the bottom of the screen and enter the text you’d like the lock screen to display when waking a device up (before you enter the passcode on the device). Then click on the Apply button.
The device will install the new wallpaper (note that devices will need to be plugged in and have be unlocked to install these new options). Now the home screen should use the new image as should the lock screen.