We have different ideas about 'drops in the ocean' :-) See this article (http://fortune.com/2017/06/28/elon-musk-china-battery/) for some numbers. Projected Gigafactory production (as more come on line) could continue to be 25 to 35% of the global production of batteries.
My father-in-law, who is a big booster of South America, feels that if Argentina, Brazil, and Chile got together they could move up the 'value chain' and produce batteries for export. I do know that much of the raw lithium comes from Argentina and Chile so I expect there is some truth to that idea.
I have no idea of where they get those digits. Chinese ministry of commerce posted back in 2015 that, the amount of battery capacity used by biggest Chinese EV makers alone (excluding PHEW manufacturers) was 16.9GWh. And the amount of battery sales to car makers make less than 10% of the market in China.
Here is an educated guess that it takes a kilogram of lithium salts to make a 10kWh battery[1]. (not my work but it looks like a reasonable process). That can help you create an estimate of how much lithium salt production is required to meet various market requirements.
It is just another way of checking various numbers. You can start from world production of Lithium salts. And remember that they are used in all lithium batteries not just the rechargeable type like we're talking about here.
I don't think the "EV" numbers are comparable to "car" numbers in China. Electric scooters and rickshaws are extremely popular there (and have a much larger fraction of their market segments than electric cars).
Source: traveling in big cities and tourist areas.
Also Musk has said that he's considering building 2-3 more gigafactories, but we don't know how fast those will be built. It could be over the next decade or so.
The "Gigafactory," is a drop in the ocean if you count noname Chinese factories, but it will be one of the biggest market players outside of China