How do you get monitor to shut off when screen is locked?
Locking your screen and putting your display to sleep are two totally different things.  Locking your screen is preventing others from accessing your desktop and does not necessarily put your display to sleep.

There are a couple options for you to immediately put your display to sleep and lock the display:

Keyboard Shortcut:  If you want to put your display to sleep, use the keyboard shortcut  ^Control⇧ ShiftPower Button.

Hot Corners.  You can also set a Hot Corner.  Just move your mouse to the desired corner and it will put your display to sleep.



The key here, to get the display to lock and go to sleep  is to make sure that you have your security settings set to require a password (from "immediately" to "8 hours").