I have done something similar on motorcycle cables but the last lower cable I put on was Teflon coated and the sheath as well.I used motor oil. I removed the cables from remote, slided a 2ft rubber hose over the brass fitting and wrapped it around the cable tightly with zip ties. Then filled the hose with oil and attached compressor with zip ties on the other. Air pressure pushed the oil through cables. Like new...or better.
Ayuh,..... Ditto,..... I lube the linkages, not the cables,.....Interesting… didn’t know lubing cables was a thing. I just assumed all control cables were sealed for life.