Safely raise both rear wheels off the ground and turn one while observing the other. If both wheels go the same direction it is an LSD, if they turn opposite directions it is an open differential. I am VERY surprised that both wheels turn the same direction on yours. I have never seen a 124 with an LSD. If it is you will need to add the friction modifier when you change the lube. Put only enough of the friction modifier in it to keep it from clicking in a sharp turn.

I am not surprised that Stan or whatever his name is, would say that synthetics are not approved. He used to seem like a very knowledgable guy until he lost his credibility by putting out that Bible book. All it amounts to is a compilation of various facts and diagrams from factory MB material. As far as I'm concerned he lost credibility BIG TIME when he put out that book. Before the book he seemed like the authority and after the book he just seemed like a robot that could read MB material.

I believe that reality is that because synthetic gear lubes were uncommon at the time of the 124 design, MB had not yet taken a position. Since MB had not officially issued anything on the subject, the robot had nothing from MB to refer to, so he printed that non committal statement about synthetic gear lube because he was totally lost with no thinking power of his own.

Make sure that you think about how you will manage to get lube in once it is empty. I have a pump on a five gallon can of lube. You probably can use squeeze bottles. Place a drain pan underneath and REMOVE THE TOP FILL PLUG FIRST! This is so that you know for sure that you can remove it so you will be able to refill it. Then pull the drain plug and drain. I think it is a 14MM socket head, commonly known as an Allen.

Good luck,