Auto parts stores sell "cable lube" and I have lubed speedo cables on other cars I've owned...usually when installing a new cable.
I will have to admit though, that a wobbly speedo needle does occur with kinked or damaged cables, and re-lubing an existing speedo cable is not a common occurrence, but a band-aid fix.
The viscocity of cable lube is somewhere between graphite lube and lithium grease so it normally doesn't leak out or dry out.
I am not aware of any permanent damage done to speedos if a cable is lubed, or even over-lubed. I suspect the worse case scenario would be that the needle wobble would still persist...
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car