I can change the wallpaper on the lock screen on my S3, but is it possible disable it completely? I can't see that in the menus, I am only able to pick a wallpaper from the gallery.
You could try and change it to a black wallpaper. There is a No Wallpaper app on Google Play, which you install as a live wallpaper. It doesn't take a lot of resources.
Install a pitch black wallpaper on your phone. Search it in Google Play Store and install the app. Then you can go to your phone's settings, device, screen, wallpapers, choose lock and home screen, then choose live wallpapers and you will be able to display the "no wallpaper app".
If you choose just the lockscreen, you wont see the application but you can only choose from the gallery.
This is what I did on my Note 2.