Lanyard, make your nephew swim. You should wear it too. if it's an issue in the surf you can get a fire starter.
As for your question, you don't lube the cable. You replace it. There are clamps available for throttle style cables in the dirt bike atv market but I wouldn't bother with a boat. Also check your steering pivot tightness.
Idle may be a factor. Mine will spin even high enough to plow but that's with a full tank. I think my idle is about 1400 right now.
I think weighting can be a factor. Usually the pipe or battery is heavier and causes the ski to lean to one side. I've balanced my ski pretty well but ignored still spins.
Try playing with a few of those options.