On my '95 Civic, what is the proper lube to spray on/into the heater control valve and cable? I recently did a coolant change, and hadn't moved the control in a long time, and the valve/cable is hard to move. No leaks anywhere, but I had to grab the little pullback arm on the heater control valve and help it close all the way, it was interfering with the A/C. The dash lever couldn't quite close it all the way.

 

Is it possible to separate the cable and valve body? If you can do that, then you can tell which is causing it hard to operate from inside.
If the cable is tight. It can be lubed WD-40? Find a clear plastic tubing that has ID similar to OD of the cable and cut to length. Place tubing over the cable and tie it with wire or something. From open end of the tubing put in WD-40 or your choice of lubricant and slowly pressurize it with compressed air. Make sure it doesn't burst on your face or the engine. In time the lubricant will go to the other end. If you could rig up an pressure regulator to work with this contraption, you can free yourself from it and go inside cockpit to move the cable to see if it free-up or not.
If the valve body is tight, you may want to replace it. Or spray WD-40?