Your best bet to understand what is going on, and possibly lubricate the lifting mechanism, is to take the interior headliner that covers the sliding roof panel out and check things out.
I know the simple roof that does not pop up in the back is much more robust and easier to fix. I am not intimately familiar with your model, but I think the general arrangement and design of the era was similar on W201, W124 and W126 chassis cars. I am familiar with my W201 assembly, which was also the simple kind, and I will describe the mechanism here. You can decide if you want to chase this down yourself, but it is pretty simple, no special tools and no special skills.
The headliner on the moving panel is slightly larger than the interior opening, so it is really hard to get of if the roof won't open. Not impossible but more challenging. I will describe the way to do it with the roof open.
Open the roof about half way or more, and then at the front edge of the moving steel roof panel, you pry the liner down. There are four or five spring clips that hold it up, and that is all. Once the liner is loose across the front edge, there are no other fasterners. Just pull it forward, and then feed it out the top, through the roof openning.
Once it is out shine a flashlight at the rear of the openning and activate the control switch to shut the roof. The cable runs in a fixed tube, and is connected to the sunroof panel by a clip that grabs the head on the end of the cable, then protrudes through a slot at the bottom of the guide tube, and then spreads out in a delta shape, with two screws, one in each "wing" that are fastened to a cross beam at the rear of the panel. This arrangement on my car failed when one screw holding the clip to the crossbeam fell out. At that point the clip could rotate about its center, which also let the cable travel a little further, enought to get the entire distorted clip assembly out of the guide tube, so it would not go back in. You will see what I am talking about when you get the access to the area.
Anyway, you will see the cable opens the roof by pulling the crossbeam backwards, which first lowers the rear of the panel and then, once the panel can move backwards the cable pulls the panel backwards, into the space between the rear seat liner and the steel fixed roof. The pivot points of the cross beam can be lubricated, and the cable can be taken out and lubricated if it needs to be lubricated.
The closing action is the reverse of the openning action. The closing runs the roof to the end of its stroke, then the cross beam pivots up and forward as it lifts the rear into position. If one side is hanging up, it is possible the crossbeam, basically stamped sheet metal, is pretty flimsy and could have bent. In this case I think you will have to replace the cross beam. I would go to a junk yard and get a whole roof panel, then swap the moving parts. If you need to, you can take your roof panel out, but I would be afraid to do that without knowing how hard it is to put back in and get it aligned. The intallation of the liner is the reverse of taking it out - feed it in from the top, through the roof hole, and then align the spring clips with the holes in the front edge of the roof panel, and pop them in the holes.
But, if you have the whole back end hanging low, cleaning and lubricating the mechanical joints/pivot points should help make it work better. Good luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)