Yes and yes, in that order!!
If they are sticky (as mine is), there is not really much hope of any lube you MIGHT be able to get down there wil do anything.
BUT first I would look at the throttle linkage on which the cable end attaches, as this can cause this if really dry, and binding, might be worth taking off and putting some grease on bolt that acts as spindle that passes through the "arm".
Be careful tightening the bolt as they are weak as poo poo, and snap(don't ask!!), and it's not much fun getting a thread out of a hole when it is only 5mm in size, without wrecking things more.
I did find on mine that the bolt(pivot), was at 90degrees to the housing but the arm was not!!, so it was trying to pull out all the time, a vice and some tools soon fixed the problem though, just have to wait for the swelling to go down now, HAMMER =1, THUMB = 0 !!!
tabetha