I am usually the guy who at the end of the evening shutting down the family PC, but these I do a lot of work on my Surface so I may not have logged into Windows at all. When I originally updated Windows 10 I was able to shutdown my desktop from the lock screen, but after recently completing a system restore I lost the option. Thankfully I found out how to enable the capability with the following steps:

  1. Hit the Windows Key, and type Local Security Policy and hit enter.
  2. Select Security Settings->Local Policies->Security Options
  3. Double click the Select the Shutdown: Allow system to be shut down without having to log on option.
  4. Select the Enable option in the popup window.

AllowSystemToBeShutDown

That should do it!

Just a note that this option does not appear to be available for Windows 10 Home.