Best way to "unstick" choke / choke cable?

[chandlerbingfl]

I've had some issues w/ my GZ getting hard to start. I think I have it pinned down to needing a battery but the major concern I have now is the Choke. The lever will not move at all, will not even budge. I removed the choke mechanism from the carb and everything looks ok but the plunger will not move as the cable is frozen / stuck.... I think the cable is frozen somewhere down the line due to lack of use. I've owned the bike since 2010 when I bought it slightly used w/ ~1200 miles on the odometer and rarely if ever use the choke.

Since it looks like the cable itself is "sealed" any way to lubricate it somehow? Is the cable hard to replace?

Thanks in advance!
Chandler