Regarding your LSD question. I'm pretty sure LSD was an option on the 535is. The "is" was a 535i equipped with, sport seats, M5 air-dam, rear spoiler, and sport shocks and springs. Otherwise it's just like a 535i. I've heard if you look at the # on the diff., and see an "S", it is LSD, otherwise it's open. Both the 533i and 535i had optional LSD's.
There is no way to turn on LSD by a control as mentioned. It's all controlled by clutches in the diff. - if one wheel spins faster than the other, the diff. sends 25% of that excess torque to the other wheel. Open diffs. simply let that one wheel spin, and transfer no power to the other wheel until you let off the gas.
LSD's can wear-out if abused. Wining or groaning noises may indicate an issue.
As said before, get the best snow/ice tires you can find. I just purchased 4 Nokian Hakkapeliitta RSi's to replace my worn Blizzak WS-15's. These tires are top-rated in two Swedish snow/ice tire reviews. The Michelin X-Ice also got great marks. All-seasons are garbage in comparison to dedicated snow/ice tires.
I have not seen a 535is that did not have LSD. You can purchase one for an E28 via the internet and I have also noticed them from time to time on EBay.
Update by original poster. The 535is now has 262,000 miles. I had not adjusted the valves in a long time; when I checked them, two where.001 too tight and the rest were perfect. Amazing. The compresion is still 160 on all 6. Really amazing. Mileage in mixed driving is 21.5 per the trip computer. Highway driving will achieve about 26 mpg. I have only burned unleaded fuel in this car and used Casterol GTX 10-30 almost exclusively.
With the right maintenance routine, a quality car like this could easily last a lifetime.
I am looking to purchase an '87 535is. It has new rear struts but needs new front struts. What will this cost me and do I need to replace shocks and springs as well... forgive me I'm not sure what each does exactly.
We have a 1987 535. It is a wonderful car. I have personally traveled with it from coast to coast. The family has now owned this car for 15 years. It is a very reliable car, and one of my family members now drives it and has no intention to ever sell it it is that good. I hope my toy (Sdrive Z4 3.5i) is that good!