Multimonitor in login screen vs. lock screen
When the screen locks, it really has no reason to display on both screens although I can see why you would want the second screen to display something. The lock screen function and login screen are programmed separately, so they will behave differently. The only thing you can do is go to Launchpad.net and find Ubuntu. Then, report this as a bug/idea. Canonical is great about considering suggestions. Include a link in the report to this page so they can see your pictures.