Get some doo dads, hose, fittings, clamps, adapters, etc etc, and get a hose that will slip over the end and clamp it to the jacket. Adapt the the other end to the grease gun/ etc of your choice and pressure feed some lube down in.
In the old days, many of us around here did not use parking brakes in winter. We get a lot of freezing slush/ wet snow, and it gets into the cables and freezes. I was just relating a couple of stories of the old days to Rusty on the landline
When I worked in Spokane (Spokamentro) I was approaching the ID-WA line, and there's a WA weigh station exit there. The day was mid winter, about 10F, and the streets had thawed, temp dropped, and froze. It was a mirror of ice. There was a slow up coming towards state line, and as I finally got my turn to pull over and pass, here was a couple of women in a Citation......dragging the stopped rear tires down the freeway!!!. It was so slick, i guess it didn't matter. I actually honked, waved, and got them to pull over. Last I saw of them they were headed off the exit to the weigh scales. This was long before cell phones