I don't know if you have completed the job yet, but for what it's worth ...
I had exactly the same problem on my '77 450SEL (116 chassis). Replacing the speedometer cable fixed it completely. My cable was housing and cable. And if they are available separately, I would replace them both anyway. Both can become worn and I would imagine they both have after the miles you must have by now.
I would be reluctant to shoot new lube in the cable before installation. The factory has put proper lubrication in there and second-guessing them may just as likely wash out the proper lube.
It's been a couple years now, so I don't remember any details, but I do remember it was straightforward and much easier than I anticipated. As I recall I didn't know what to do with the rest of my Saturday afternoon* I'm sure I found something else on the car to fix**
I also recall that when talking to the speedometer mechanic, he mentioned that wear on the bushing the speedometer needle shaft fits through can also cause jumping. This is the cause I suspect on the same behavior on my '88 Volkswagen 136k mi. On it I just replaced the cable and although jumping is much less, the speed fluctuates to 10-20 mph higher than actual at highway speeds. To fix this you would need to remove the speedometer and send it to or leave it with a speedometer repair shop for the modest repair.
Good luck with your repairs*