There's products made specifically for cable lubrication. But once there's a noticeable problem. None of that stuff really works. Maybe its okay for maintenance, but it won't fix a bad cable. A new cable isn't exactly expensive. So that's the only way to go here.
Sometimes fishing that cable, or trying to duplicate the routing. Especially after removing the old cable, can be a problem. I'd probably try to tape the leading end of the new one, to the trailing end of the old one. Then work it through. That way it'll go over what its supposed to, and under, or through the rest. Hopefully leaving it positioned just as it's supposed to be. Might work, might not, but it's worth a try. Don't forget that its likely clamped down in a place or two. Good luck.