I did alot of research and you have to use a 80w 90 mineral based gear oil if you have the Auburn limited slip. My opinion on Lucas oil is that it is junk. I had it in my other truck and when I went to change the fluid it came out very foamy. Here is a link that shows why
JHZR2 & wm1998: I know exactly why this company cautions against synthetic and I got it from the horse's mouth. Here's the skinny.
This is a cone clutch limited slip, currently the only such unit on the market. Instead of clutch plates, it uses a cone shaped member combined with the side gear that fits into a recepticle and the friction between those two parts is what provides the axle torque (braking) for limited slip operation. You can see an exploded view of the unit here, as well as an explanation on how it works:
The bias ratio of the unit is calibrated on a certain friction coefficient, so the first thing that happens with a synthetic is a loss of bias ratio (the unit is less effective). The next thing that happens is a polishing of the active surfaces of the two clutch members and this further reduces the bias ratio. Once that surface is altered, that loss is permanent. Unless, I am told, you dismantle the unit and rough it up again. I was told that Auburn Gear has experimented with some types of synthetics. I was told that they are looking into the issue again and if I hear anything, I'll pass it along.
How do I know this? Look at the byline on the attachment.
To the OP, I would use a 80W90 mineral. That's what the engineers at Auburn Gear installed into my truck when they installed my unit. The 2.5 and 3.5 bias ratios Auburn advertises are calibrated on a Chevron 80W90 gear oil, so you'll get the advertised performance on that oil... with the correct amount of friction modifier of course (which comes with the unit).
Does RP have any non synthetic oils? I don't think so, nor do I think there are any non-suyn 75W140 oils.
PS: wn1998: Detroit recommends mineral oil for Truetracs as well. Synthetic do reduce the bias ratio of that unit as well because friction is what is'a all about in that apparatus. There can be adverse symptoms too, such as odd noises and squealing but not always. Anecdotally, we know some syns produce no adverse noises in Truetracs, Amsoil is one. I have a Trutrac in another truck and had Amsoil in it for a time with no noise. Someone at Eaton knows more about which oils cause this but they won't name any names. Rumor has it that it's Redline, but I have never been able to verify that. Any Truetrac owners out there running Redline?