It has been about ten years since we had a cable dump valve but I made a fitting to grease the cable.
I used a 1/4" or a 1/8" pipe coupling to screw on the threads where the cable was bolted on. I had to take the handle off first. Then I screwed on a short piece of pipe, then an another coupling, then a grease zerk. Use the grease gun to pump grease into the cable.
I put a rubber o ring on first because the treads would not keep the grease from leaking out too fast to get in the cable very far.
This is kind of messy but I only had to do this one time in three years.