Go to a motorcycle shop. Spend about ~$15, buy the cable lube kit that comes with one of these things and a spray can of oil.
Use it once, and question your sanity for not having bought one many years ago.
Seriously, I've had one for years, and it works far better than anything else I've ever used or done to lubricate cables.
The best thing you can use on this is special-purpose cable lube (from a motorcycle shop) or dry moly lube if you can't find that.
Holy mercy! How do they not know about these things in the world of pedal bikes??!!
Is that thing big enough to do e-brake cables?
Holy crap, how did I miss this tool? Very cool.
Yep, we used those at my old bike shop all the time. Had to buy them from the motorcycle shop though, the distributors in the bicycle world couldn't get them.