Yes, lubricate by all means but if the cable is connected to the surging issue that cable+housing is possibly really defective and in that case, you should replace it. It Could be a broken strand inside, catching the housing and that is dangerous....if a bunch of rust comes out when you are oiling it, turf it and replace.
a bit different issue, but Ive had this cable-routing issue myselfwhere turning the bars pulls on the throttle. I used pull-ties to hold it to the frame under the tank once I had it so moving the handlebars doesn't affect the throttle. It can be difficult to get it the routing just right and when I use the adjustment at the handlebars to (temporarily!) adjust the idle, the "turning acceleration" can show up again on one bike even now.... Oh, usually, it wouldn't cause surging unless it's in the parking lot making sharp slow turns but that's not so safe either...
I wonder if Possibly somebody has put taller handlebars on without lengthening the cable ...?
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