Wow, there is a lot of speculation in this thread.
Pretty much everything MB Doc has said is absolutely correct. No W123 was available anywhere in the world with limited-slip from the factory, but yes some may have come from AMG with limited-slip. (And probably a G-T LSD, if it was from AMG.) Or someone may have installed an aftermarket conversion. If it's factory LSD, the VIN will show option code 256 in the datacard, and no, that is
not stamped anywhere on the diff. There will be a little metal tag under one of the diff cover bolts, with German text specifying special diff fluid. That's it.
For the record, the only models I'm aware of that came to the USA with true LSD are the 116 6.9, the 190E-16, and all 560SEC/SEL models. The end. A handful of 124 and 140 diesels, and also a 202, had optional ASD, which is an LSD plus some hydraulics to allow 100% lock under 19mph when wheelspin is detected. ASD was more common in Europe than in the USA. The vast majority of US cars with any kind of traction control used ASR, which was an electronic simulation of LSD, but ASR cars have open diffs. ASR will reduce throttle and/or apply the brake to the spinning wheel to mimic the effect of LSD, without pesky diff clutches to wear out.
Tom, about your project: Yes, the large circlips are of various thicknesses, and yes they are used to adjust the backlash. However, they are ALSO used to adjust the bearing preload! You need to measure & set both backlash & preload. Now, I know you're dead set on using the 3.27 LSD carrier with your 3.69 gears, but if it were that easy, Mercedes woudn't have created a different part number for a 3.69 LSD carrier. I will almost guarantee that you won't have enough adjustment with the circlips to correct the backlash with that setup. If you're lucky you might be able to have a spacer machined, but it will be a full custom job. Let's hope I'm wrong though.
Finally, about the friction discs. Ordering 3.2, 3.4, 3.6 is too wide of a spread. If you studied the photo below, you'll see that with the rest of the clutch pack replaced, the tolerances on the end discs were in hundredths of a mm, not tenths. I tried going up +0.2 from the old ones, for the same reason you did... "to make up for wear"... but they wouldn't fit AT ALL. Even +0.10 was too much - it would assemble, but refused not rotate; it would bind up. If your worn disc(s) are 3.2 (or less!), then +0.40 is
way too big. The good news is that you can machine the back side to make them thinner as needed. I had to shave off a couple of hundredths at a time until it worked properly, which ended up at +0.05 (+0.07 was still too much). Also, remember that the thicknesses may be different left to right... if so, you must retain the delta between sides! Othewise you'll end up with one side too loose, and the other too tight. Note that mine were 0.10 different left to right. I don't know how to measure that if you lose the factory baseline, so I hope yours are the same, or your tech wrote down the number as he took it apart.
