Span Wallpaper Across Displays in Lockscreen

Solution 1:

At this time this is not possible due to bug #1291359.

This issue is still present up to Ubuntu 16.04.

The most common thing to do at this moment is to show the default login screen/color.

You can do this by installing dconf Editor.
Open a terminal with Ctrl+Alt+T and type:

sudo apt install dconf-editor

or click dconf Editor to auto-open Software Center and click Install to install it.

Now we must grant LightDM permissions to access dconf Editor.

• Gain root access, type your password (no visual feedback),and Enter.
  sudo -i
• Allow user to create a connection to the X server for lightdm
  xhost +SI:localuser:lightdm
• Switch to user lightdm
  su lightdm -s /bin/bash
• Start dconf Editor
  dconf-editor

On dconf Editor, navigate to com > canonical > unity-greeter in the left pane.

• Disable (untick) the value for 'draw-user-backgrounds' on the right pane.
• While at it, you may want to disable 'draw-grid' (it disables the dotted grid layer).

Reboot to confirm changes.

sudo reboot

Note: from now on LightDM has permission to access the X server, so every time you open dconf Editor, LightDM already has access.
To revoke this access, issue the command xhost -SI:localuser:lightdm as root.

Solution 2:

Hm. To save you some poking around, I've tried Variety, dconf-editor, nitrogen, and CompizConfig with no luck. The closest I could get was setting a particular wallpaper for just the lock screen with dconf-editor.

Strangely, if you install gnome-tweak-tool there is a setting under Desktop that allows you to choose a separate mode and image for the Background and Lock Screen - but while the Background settings here affect my desktop, my tests with the Lock Screen settings don't make any change. It may be a lead, however, if you want to try and finagle Unity into submitting to Gnome (assuming the tweak options haven't just been broken from the start).