A trick I've used for years on older cables I didn't want to replace, or just a basic servicing is: Cut the bottom corner out of a zip-loc bag, just big enough to slip the cable into. Tape or tie-wrap the bag as tightly as you can around it, so that the cable is in the bag. Fill the bag with a light oil, seal the top, and gently squeeze the bag. You can still work the inner part of the cable up and down in the bag as you do this, and it'll give you some "positive" pressure on the oil, "injecting" it down through the cable.
Now I rarely get the bag sealed 100% around the cable housing, and sometimes it'll end up looking like the Exxon Valdez has just wrecked in the cockpit, so keep some rags handy. Maybe a bed sheet. You'll cuss me for this, but it does work..