Found a way for KDE 4 (up to Ubuntu 14.10). For modern KDE 5 see other answer.

1. Go to System Settings → Application and System Notifications → Manage Notifications.

2. Select Screen Saver as the Event Source

3. Locate and select the Screen Locked

4. add this command to the event:

    xset dpms force off
   

It will turn off all displays every time it gets locked.

I can offer a workaround to this

Never mind the settings in the GUI, you can lock your screen and send your screens into standby via the command line

To lock your screen you could use

gnome-screensaver-command -l

or (if don't use gnome3)

xdg-screensaver lock

and to turn off your monitors (standby) you could use

xset dpms force off

Now, since you don't want to do this manually, but after a couple of minutes idle time, we need to find out how long you have been idle. This can be done with xprintidle

sudo apt-get install xprintidle

xprintidle will return miliseconds of (xserver) idletime

Now, lets combine this into a script(*). Use your favorite editor to copy/paste the following, modifying the IDLE_TIME to your liking

nano /home/yourusername/idle_stby_lock_screen.sh

#!/bin/sh

# Wanted trigger timeout in milliseconds.
IDLE_TIME=$((5*60*1000))  # replace the '5' with how many minutes you'd like


# Sequence to execute when timeout triggers.
trigger_cmd() {
    echo "Triggered action $(date)"
}

sleep_time=$IDLE_TIME
triggered=false

while sleep $(((sleep_time+999)/1000)); do
    idle=$(xprintidle)
    if [ $idle -ge $IDLE_TIME ]; then
        if ! $triggered; then
            gnome-screensaver-command -l
            export DISPLAY=:0; xset dpms force off
            triggered=true
            sleep_time=$IDLE_TIME
        fi
    else
        triggered=false
        # Give 150 ms buffer to avoid frantic loops shortly before triggers.
        sleep_time=$((IDLE_TIME-idle+150))
    fi
done

Then make it executable with

chmod +x /home/yourusername/idle_stby_lock_screen.sh

You can test it out on the commandline

/home/yourusername/idle_stby_lock_screen.sh

if you are content with it, you can add it to the startup of your Ubuntu, like described in these answers here or with the "Startup" app in Ubuntu - just make sure to use the absolute path to your script.