2.87 lube?

All you need is a quality hypoid gear lube that's rated for limited slip differentials. 

I use a synthetic hypoid lube that's rated for limited slip - always have, never had any chatter or bad things happen. Most these days actually are rated for limited slip differentials and that includes pretty much anything made today and back 40-50 years. In the old days when most lube was not rated as such the additive was required. It was also cheaper for shops to by hypoid lube bulk then add the additive when or where required. These days you'd have to look on the auto parts store shelf to find a quality lube that doesn't say on the bottle that it's rated for limited slip. 

I have not used additive for years, but then I buy hypoid lube that's rated for limited slip. That's what is in my 3.15 that's under my 390 Javelin - it's a synthetic which is all I run these days. All of my differentials get synthetic. 

Read the bottle you lube came in - if it doesn't states it's for use or meets all requirements for limited slip, add the additive. If you have no clue what's currently in the differential, add the additive unless it's an "open differential". It's either an open differential or it's limited slip - one needs the lube intended for limited slip, the open differential does not. 

It's really that simple today. Anything else is bringing up "the old days" when even decent lubes didn't do well with limited slip.