Lube the cable with something like Vasoline. Should do the trick. Don't use a heavy grease.
I have had lots of old cars and bikes, this happens quite a lot. Just don't look, if the Vaseline doesn't fix it! But, I agree in principle, very light lube needed, I would go for something even lighter, take out the cable inner, clean off well with WD40, and leave it without any additional grease. It is probably stick / slip in the cable.