According to data for the year 2016, four countries dominated lithium-ion battery manufacturing, having 97% of the total production capacity: China, the United States, Japan, and South Korea.
The top player was, of course, China with 63% share but "only" 44% was for automotive applications.
A positive surprise is the second position of the U.S. with 20% of global automotive lithium-ion battery manufacturing capacity, mostly thanks to the Tesla Gigafactory (a joint project between Tesla and Panasonic). In the case of the U.S., 90% of all lithium-ion cells are for automotive applications.
Source: Mayyas, A., D. Steward, M. Mann. "The case for recycling: Overview and challenges in the material supply chain for automotive li-ion batteries." Sustainable Materials and Technologies 19 (2019).
One thing not mentioned for the 2016 snapshot are massive investments in battery production in Europe, which in the next few years should shoot the European Union into second place.