A lecturer is hard to understand, what to do?
As a lecturer in Asia, I appreciate what you are saying. I have some colleagues who are Asian who are quite clear when they speak English and others with whom I require a minute or two to even recognize when they are speaking English because their accent is so strong. You have to work with what you've got.

While you could confront your lecturer, as snim2 said in an answer, you need to be delicate about this. The lecturer could find you condescending or insulting. Even if the lecturer does not think you are being purposefully hurtful, making a lecturer self-conscious about his accent might make him an even worse lecturer (of course, it could help, depending on his personality).

I would recommend talking to the lecturer and simply say something like this: Hi teacher, I'm finding it necessary to read more about this topic in order to do well in your class. Could you point me in the direction of some reading material that I can use to improve my understanding of your subject? (then stop talking)

Once you have the reading materials, focus your learning there, perhaps with some genuine emails to your lecturer, if he allows.

Even the lecturers I've met with horrible English will happily go out of their way to find some material for you to read. Either they will recommend a textbook, some articles, or they will have some material they have collected on their own. I don't believe I have ever met a university lecturer who would be offended by this approach nor have I met one who would not support a student with such a request.