I would suggest you ONLY buy a diff from a VY - don't just buy any old LSD from a late model commodore.
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I have an LSD fitted to my VY supercharged V6 auto as I ordered the car with this option.
1. Make sure when you inspect the diff it has a metal tag attached to the rear FILLER PLUG with the words imprinted on it as follows:
"LSD USE APPROVED LUBRICANT + FRICTION MODIFIER"
If the diff does not have the metal tag attached then do not buy it even if the seller swears it is an LSD.
2. The LSDs and standard diffs set up for the VYs have an identifying code.
There must be a white sticker on the driver's side of the diff housing. This contains various codes, the diff serial number and the diff ratio. The sticker does NOT say if it is LSD though. Only the metal tag has this info. Do NOT buy a diff if the white sticker has been removed or if it is damaged and unable to be read.
The diffs fitted to the VYs have code "FH" imprinted in large letters on the white label together with an 8 digit number. This sits above the Serial Number.
Below the serial number on the white label is the diff ratio. The autos with LSDs all had a diff ratio of 3.08 or 3.07. (Mine is 3.07). So did the auto/manual V6 and the auto V8 cars with the standard non-LSD diff so you cannot identify whether a diff out of an auto is LSD solely from the diff ratio.
(The 6 speed manual V8 VY cars came with a much lower diff ratio at 3.46. Fit this on an auto and you will be running the engine too fast in all gears at normal road speeds and your economy will really suffer).
I would be very wary about buying a used LSD off ebay or from a similar source. There are many damaged and clunky noisy diffs that have been removed from thrashed commodores and sold off to unsuspecting amateurs on places like ebay. Unless you are a diff expert you will not be able to identify a good one from a dodgy one when it is off the car. Diffs are expensive to repair so if you buy a bad one you will be throwing away lots of good money.
I would contact a reputable diff specialist in Sydney and discuss your plan with them. These people are much more likely than you to locate a good serviceable diff for your car, fit it up for you properly and guarantee their work.
A diff is a critical and major section of the driveline and if you cannot afford the cash to have it done by a professional I would leave it alone.