The Lock screen, new to Windows 8, is a fancy feature which allows you to display an image while your PC/tablet is locked and displays other useful information.
However, when the PC is locked, the normal display off timeout value has no effect on it and you cannot specify the timeout value after which the screen will turn off while you are on the Lock screen. Turns out, there is a hidden registry setting for this and enabling it even turns it on in the Power Options control panel GUI - the same window where you specify other power related timeouts. Let me show you how.