From what I can see, a good cleaning with a solvent of some sort, PB Blaster sort of thing, and then a couple shots of WD-40 or similar, would do wonders for the operation of the latch. Might even solve the entire problem.
There's an awful lot of dirt caked in the moving parts you show in your pictures. A dental tool, or other small, pointy, item would do a lot towards being able to clean the dirt out. Then, once again, some oil of some sort might be the solution you need.
Once it's clean and oiled, actuating the latch from inside will get the oil worked into the cable. Problem solved.
Good fortune to you!
Pat☺