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I would not lube it with anything except graphite. Any liquid based lube or grease will attract dirt and dust which will cause you problems in the long run.
I assume from your other thread you mean the one from the handle to the splitter? It's fully enclosed in the cable housing, except at the ends. The only way to lube it is to take the upper end free and slowly trickle oil down in there. If it doesn't move easily, then spray brake or carb cleaner down the housing while working the cable. Then lube. Any kind of motor oil should work fine. The best thing is to use the e-brake often, when unused they get cranky.
If you set the brake it will give you a little play between the cable and the housing. Take your can of WD 40 and fill it up. Let it slosh around in there while you drive.