The outsides may be peeling from the use of engine degreaser and engine heat.

A cable slides in a smooth sheath. Nowadays they are built with a polymer liner and a good for a long time unless dirt infiltrates from the ends. For this reason I would not apply any substance that would attract dust. At best, a silicone spray may be the only lubricant to use and then it may carry in dust with its solvent carrier.

Since the outer covering is going bad then there will be a demise in the future because dirt will start to penetrate to the inner shield.
If there is a worn spot somewhere on that inner liner then it will start working at fraying the strands of the cable. When that happens it will become harder to move and may get sticky and at that point you are past where you should have replaced it.

If you are turning the spool with your foot and the cable drags any at all on the return srtoke, then I would advise to change the cable out.

Phil