How to enable auto-screen update on monitor plug-in/out on Lubuntu (Also, how can this be achieved in Ubuntu)?

It is probably a Gnome or Unity feature which is absent from LXDE. You could probably write a udev rule to do this on monitor disconnect.

I have written a little script that will detect the monitors and extend accordingly:

#!/usr/bin/env bash

xrandr | grep VGA | grep -w connected >/dev/null
echo $?
if [[ "$?" -lt 1 ]]
then
    notify-send "Extending desktop to VGA screen"
    xrandr --output DP-3 --auto --output VGA-0 --auto --right-of DP-3 --primary
else
    xrandr | grep DP-2 | grep connected >/dev/null
    if [[ "$?" -gt 0 ]]
    then
    notify-send "Extending desktop to DisplayPort screen"
    xrandr --output DP-3 --auto --output DP-2 --auto --right-of DP-3 --primary
    else
    notify-send "No known screens found"
    fi

fi

You need to have xrandr installed but you almost certainly do. You will also need to change the monitor names accordingly (in my case I switch between an external VGA and and external Display Port display). Run xrandr with your external screen connected to getthe right name or update your question with the output of xrandr and I can help you with it.

I have mapped this script to be run with a keyboard shortcut and simply run it whenever I connect or disconnect a screen.