I want to extend my L visa for the second (and last) time. Is it possible to extend with a single entry?

I'm afraid that it is hard for you to get a single entry visa within China, generally speaking, if you want to apply for extension within China, it is generally 0 entry visa with a period of stay duration. Anyhow, you can go to the local exit-entry administrative bureau of public security bureau to have a try, if the application is denied, you can apply for a new visa in the country which you will go, then return to China.