Though I don’t condone (nor condemn) opening the controller, if you do you should look here to see what your in for:
Good white lithium and Teflon greases are non-conductive, however, I would not recommend greasing the joystick.
What you can do is check to see if the plastic has burrs that are causing sticking. Cut a piece of paper to 2" by 1/4". Push the joystick to one side and slide the paper in the other. DON’T PUSH IT IN ALL THE WAY. As you slide the paper around the circumference of the gap, rotate the joystick. You may need to slide the paper back and forth. If this feels smooth then the problem is likely inside the joystick’s potentiometer spring-back mechanism.
I don’t think you can fix that. So, you will have to ask VEX how much this type of repair costs. My guess, it is not much more to buy another controller.
Here is a joystick that is similar to the one in the controller for reference. As you can see it is not replaceable by the user.