Reply to "Replacement speedometer lubrication"

...ofcourse, You must Lubricate it! That's why Your Doing it a Second Time! Grease it up as You slip the Cable into it's Sheath. The 'Law' is, You NEVER Run any Metal against Metal, Dry!!
When in Doubt, Lubricate!!

I don't like Graphite, it's for use in Locks.

When installing a New Cable, You Grease it up with Teflon Grease as You slide the Cable into it's Sheath. Teflon Grease is Thin and Does Not Freeze.

If You want to take the 'Easy way Out', the Cable You have now, MAY be saved. Unscrew the Cable at the Transaxle, Hold up the Sheath and Squirt some 5 Weight Oil down into it with a 'Oil Squirter'! Wait a few Minutes and squirt some more in. Reassemble the Connection back to the Trans. Drive the Car. The 'Screw Action' of the Cable, itself, will flow the Oil all the way to the Speedometer; when in Use!
I did that Years ago, My Original Speedo Cable, Still runs Smooth and Silent, after 58,000+ Miles!
Be advised, the 'Jumping' of the Speedo Needle can also be caused by a Broken Tooth on the Nylon Drive Gear! AND I DO NOT recommend removing the Drive System from the Transaxle to Inspect for it!!...