There are motorcycle cable lubricators that are used to get lube inside the cable sleeve and not everywhere else.
The idea is to clamp the cable sleeve end w/the ferrule into the rubber sleeve, the inner cable comes out the other end. Tape or whatever can be used to build up the OD of the type cable being worked with.
Then the lube straw tip is inserted into its hole and the lube is injected into the cable sleeve.
Cost <$10. Many bike riders will already have one around the shop.