U got that right...if u have a stock engine the OEM LSD gearbox is not an issue and probably don't need to upgrade...but for high power u do need a good one
When I put a bigger engine in my car I used the same LSD gearbox from my stock engine...the power gain was from 65hp to 342hp, I know it was a big mistake as the OEM LSD was only designed to handle a maximum of 90hp, two weeks into my test drives I broke it and now last weekend I've put a aftermarket LSD gearbox I bought for over a grand which is rated for 550hp+ fwd....
As far as the lubricants are concerned, buy THE EXPENSIVE AND BEST PERFORMANCE GEARBOX OIL and put it in...u won't need to refill/change for a long time unless it leaks...