Personally I'd leave it alone till you need to lube it. I would no way pour motor into one end of the sheath, just make a mess. Keep in mind a speedo cable is just a long spring and if bad and causing a bouncy needle, it's not the cable rubbing on the sheath. It's crud, rust etc in between the coils of the spring that bind/catch/release that causes the bounce. If you want to lube the cable, remove it from the sheath. Clean it well. There are dedicated "speedo" cable lubes that work well if applied correctly. but speedo cables are different construction/function than throttle, clutch etc cables. I prefer a light machine oil, spindle lube etc. 3-in-1 oil works great and easy to find. With a cleaned cable I'll massage the lube into the coils of the cable with my fingers to insure it gets in there where it counts. There are dry speedo cable lubes(powdered graphite) that work well on a clean and dry cable. Still gotta work it into the cable not just spritz it on the outside. Then wipe off any extra, any extra is just going to gum things up. If you're going to be riding in extreme cold, no way would I use any type of grease.
Just my two cents worth.