I've lost most of my German, but in my mind it is a much more literal language than English. In English we play games with sounds, so yes Ritelitz likely indicates how a word sounded to English ears. But I'm not sure I would jump to Reudnitz because it also sounds similar. I don't think the German language plays the same sort of word games - the meaning is important. So I would also look for a place name that is related to the meaning of those sounds.
Just thinking at my keyboard, the litz means "Line", and so does your " ältere Linie". In fact the place name might simply be a version of Reuss-lizt (which can also be spelled Reuß) - equivalent to Fürstentum Reuß ältere Linie (or the Reuss Elder Line Principality). Maybe the name of the principality was specific enough.
Then it could also refer to Greiz, which I'm reading was the capital.
It does give you a specific focus for the research though. It might help to find a historian who researches Germany at this period. Food for thought.