If the cable is winding and unwinding evenly, it's most likely something, somewhere, is sticking, and not working as smoothly as it's supposed to. Any lift I've ever worked on is a pretty simple affair. Actually, REALLY simple! Absolutely no rocket science involved or required to fix!
They are chain driven for the most part. If that chain is all dried out and rusty I suppose it could be making some noise or causing a jerky action as it goes over the gears. The pulleys that the cables run on that haven't been maintained could be trying to freeze on the shafts and causing some issues there as well.
The hardest part of this project will getting started on it. Once you dive in and get your hands dirty, I'll be surprised if the issue takes much to find. Start by making sure all moving parts are well lubricated and working smoothly.