I can't find any working way to download kdz from LG servers for now.
UPD. Try to download LG Mobile Support Tool from here:
http://tool.xcdn.gdms.lge.com/client/app/B2CAppSetup.exe
Then install it and open.
THE PHONE HAVE TO BE UNPLUGGED FROM PC!
Now press "Install USB driver" - choose your phone model - it will install required drivers, you'll need to agree with installations and maybe run files from some opened archives. (IDK why, but I had to)
When all installations are done, change in the phone: Settings - Connect to PC - change to LG software mode.
Now plug the phone in. It will install drivers and detect the phone.
Now in LG Mobile Support Tool press Options - Upgrade recovery.
It will download kdz file for your phone and fully reflash your phone.
To get kdz and not to reflash the phone you can click "Upgrade recovery" and unplug the phone. It will download kdz for your phone and ask what to do.
Minimize the window and go to to C:/ProgramData/LGMOBILEAX/Phone/
Here is your kdz!