"Window regulator" would be the correct terminology, if it were a Ford. I used to work for Ford Motor and that's what they called them (at one time I had design responsibility for the Window Regulator Handles on all Ford's car lines - what an awesome responsibility!!!).

Thankfully, I have had no trouble with my windows on my 240D, but my previous experience with Ford would tell me that you are on the right track. Hardened stiff grease on the gear and on the sliders will slow the windows down to a crawl. The Ford motors have circuit breakers that limit current draw. This why a window may stop working for awhile and then work later, when the circuit breaker cools off. Power window operation is especially troublesome in cold weather when the lubricants get thick. We had a cold room where we tested the windows, and the ultimate test for new designs were cold room operation. We used to sell a special silicone based window regulator lube that worked great, even in cold weather, but it was not allowed in the plants, because silicone and new paint are not compatible.

Good luck with your windows.

__________________
1976 240D
1987 560SL
2007 E320 Bluetec
1998 C280 (now son’s car)
1982 240D Manual - Sold