Just to be clear, I'm not a chemists. This is just what I have learned from following this industry. Any real domain expert feel free to correct or expand.
Lithium comes in many forms, on a high level there are 3, hard rock, clay and brine.
Hard rock was initially common, when lithium was new and was mined in North Carolina. It turn out it was cheaper to produce lithium from brines in South America. This basically means pumping salty water from below the earth and using the sun to evaproate the water [2].
However since the battery revolution, Australia has been a leading miner of Spodumene [1]. This then shipped to China and turned into lithium chemicals.
Clay has not yet been exploited, but many are tying (like Tesla showed in their presentation). Another technology much talked about is Direct Lithium Extraction, that simple extracts lithium and releases slightly less salty water back into the environment.
From these mining operations two different chemicals are produced as input for battery cathode refining processes, lithium carbonate [3] and lithium hydroxide [4]. Different methods of mining and refining produce either of those. If my understanding is correct, most brine operations end up being carbonate and most hard rock operations end up as hydroxide. Often hydroxide is also produced from carbonate as a follow up process.
Depending on your cathode material and your process you need carbonate or hydroxide of specific quality. And because the material performance here is so important and the battery as a system is so sensitive, even the slight changes in source material and the process can have large impacts. Even the slight changes in source material and the process can have big effects.
So that means if you have a mine, you can't just mine do minimal refinement and then throw it on to the international standardized metals market the way it works for other materials. You need to build a highly sophisticated chemical processing facility that can handle your material specifically and produce high quality materials in a sufficient quantity that car makers can go threw the many rounds of testing that are required before a new source material ever makes it into a car.
Since the lithium industry is comparatively so small the necessary expertise to do these things is not at all common. A few companies can do it and that's not very many people. So getting a team together that can pull of a major project like that isn't easy.
Some media sources that do lot of good reporting:
Global Lithium Podcast - https://www.globallithium.net/podcast - Opinion-ed Insider and Interviews
The Limiting Factor - https://www.youtube.com/@thelimitingfactor/videos - Well researched videos on batteries but also lithium supply chains. Also some interviews with experts.
[1] https://en.wikipedia.org/wiki/Spodumene
[2] https://upload.wikimedia.org/wikipedia/commons/c/cd/Lithium_...
[3] https://en.wikipedia.org/wiki/Lithium_carbonate
[4] https://en.wikipedia.org/wiki/Lithium_hydroxide