If you're in the US, forget about even trying to fit a LSD into a US version MT as apparently they're different than the Euro version. According to a guy here a while back, the Euro diff. on their MT just unbolts from the trans. On the US MT, to remove its diff. requires removing the trans from the car and splitting its halves as our MT diff doesn't just unbolt.
Auto trans? No way unless you want to try paying a trans shop who'ld be will to try it with no warranties or guaranties. I doubt that anyone would try it.
IMHO, it wouldn't be worth the hassle. No 850 has so much torque from a dead stop where one really needs LSD like true performance RWD cars do.