Is there a way to lubricate the speedometer on W124?

[jbach36]

If I press my accelerator to the floor (trying to get up a hill or something) it's a bit slow to come back up which is scary. There's about a 1 second delay. I'm assuming the original grease from 1991 has hardened and become like peanut butter.

Is there some feasible way to lubricate the accelerator cable? (not the speedometer cable. I put that in originally but can't edit it)