What should I do if I want to do a PhD at a particular lab but cannot secure a scholarship?
Talking to your prospective advisor is the best option as they should know what other funding opportunities there are. If you demonstrate determination to study a PhD with them and enthusiasm for research they will most likely try harder to find you funding and support you in the mean time. Try to develop ideas for the PhD, think about what you really want to research. Volunteering or working temporarily for the advisor could be a way in to potentially get a publication. If you can get your name on a publication, you will be much more likely to secure funding. But I suggest you call the professor instead of emailing, especially if you are not comfortable writing the email. 

As @Sayan mentioned, making multiple applications to different laboratories is also a good idea. International tuition is often crippling, but there might be better funding opportunities in another country which could take care of that. Letting the potential supervisor know you are doing this will further demonstrate your enthusiasm for research, and taking up an offer elsewhere does not mean you will never work with your first choice.