I use a cable lube for motorcycles. There is a tool just for doing cables. It can do different size sheaths. Grommet has steps in it. Yours may already be beyond saving if stuck. But might help with future cable maintenance.
Hope this link works. Not promoting this one in particular. I use cable life and like it very much. But there are many out there.
http://www.aerostich.com/cable-luber-lube-kit.html