FWIW I have tried "limited slip ready" lubes a couple of times without additive. Most recently Mobile 1 xxw/140 synthetic. The bottle clearly claimed "limited slip ready, no additive required".

After some driving it started catching and making noise. I sucked a little lube out and added the friction modifier and it was fixed. Regardless what the label says, I think they need the additive, at least with a clutch type sure grip.