Instructions

LightDM apparently supports a VNC server out of the box; however, it’s designed to work with tightvncserver (or similar) which create separate X sessions (the 2nd lot of VNC servers I mentioned above) so not quite what we’re after1.
Ubuntu derivatives use Upstart (upstart.ubuntu.com) to manage startup processes - LightDM (and GDM!) creates a login-session-start event when the display manager is up (i.e. when X is all loaded, but before you’ve logged in) so we’ll create an upstart job that listens for that, and starts a VNC server on the existing X session, allowing connections before login.

Step 1

– we want the VNC server to have a password, just in case – the VNC port shouldn’t really be exposed to the outside world – it’s easy to wrap it in an SSH connection to encrypt everything for you (see here for a good explanation of how to set that up).
$ sudo x11vnc -storepasswd /etc/x11vnc.pass
This will prompt you for a password to (lightly) secure your VNC server.

Step 2a

(for LightDM – XUbuntu, and all Ubuntu variants 12.04 onwards) – create the upstart job. Put this in /etc/init/x11vnc.conf :
start on login-session-start
script
/usr/bin/x11vnc -xkb -auth /var/run/lightdm/root/:0 -noxrecord -noxfixes -noxdamage -rfbauth /etc/x11vnc.pass -forever -bg -rfbport 5900 -o /var/log/x11vnc.log
end script
Note: if you’d like this to work with GDM instead, you’ll need to find where GDM puts its MIT-MAGIC-COOKIE – I believe it’s /var/run/gdm/auth... or something similar, although I haven’t got a box to test it on

Step 2b

(for lxdm – LUbuntu) – LXDM doesn’t seem to emit the right event, but instead is has /etc/lxdm/LoginReady which lets you specify pre-login events. However, we need to first get the xauth setup properly. Edit /etc/lxdm/lxdm.conf and uncomment the line:
xauth_path=/tmp
This specifies that we’re going to use a different xauth path; we also need to update the /etc/lxdm/LoginReady file with our x11 command, using the updated xauth path.
Put this in /etc/lxdm/LoginReady:
/usr/bin/x11vnc -xkb -auth /tmp/.Xauth1000 -noxrecord -noxfixes -noxdamage -rfbauth /etc/x11vnc.pass -forever -bg -rfbport 5900 -o /var/log/x11vnc.log

Step 2c

(for mdm – Mint LMDE)
Mint LMDE (Debian edition) doesn’t use the upstart things; instead, put this at the end of /etc/mdm/Init/Default:
/usr/bin/x11vnc -xkb -auth /var/lib/mdm/:0.Xauth -noxrecord -noxfixes -noxdamage -rfbauth /etc/x11vnc.pass -forever -bg -rfbport 5900 -o /var/log/x11vnc.log
Note that this uses the auth path for mdm which is /var/lib/mdm/:0.Xauth

Step 3

– Done!
Reboot! That’s all there is to it – hopefully, you’ll now have a shared VNC server which connects to your main desktop X session, running on port 5900 using the password you gave, all started automatically as soon as LightDM asks you to login. Hooray!
1. If you’d like to have a separated VNC server running too you can – make sure you have tightvncserver installed (or similar) and then put
[VNCServer]
enabled=true
port=5901 # I've used port 5901 so it doesn't interfere with the setup from above
in your /etc/lightdm/lightdm.conf then reboot – should have a separate X session available for VNC’ing into.

Quoted: http://seb.so/vnc-from-boot-without-logging-in-ubuntu-lubuntu-xubuntu-and-mint-lmde/