Are the Korean battery makers like LG competing against CATL and...

Are the Korean battery makers like LG competing against CATL and BYD which both have a combined 52% market share?

BYD makes its lithium batteries largely for its own use, CATL makes them for primarily the Chinese EV market too.

LG is serving the US market, not China.

Why wouldn't it be in the interest of LG, CATL, BYD and Tesla to want lithium price to remain low?
Cheaper lithium inputs make cheaper batteries and cheaper batteries make cheaper EVs, cheaper EVs mean more sales and EV growth which helps boost demand for more EV batteries.

Lithium producers are at the bottom of the food chain, they depend on a thriving EV market as battery producers do. But most of the lithium is consumed in China because that's where the bulk of EV batteries are made.

Chinese EV production cost is some 20-30% lower than Western EV makers (per Michael Dunne) and as EV batteries make it the large part of EV cost, Western EV makers would have all the desire and need to have access to cheaper EV battery technology to close the gap and advantage the Chinese now holds. Renault recently announced moving into LFP batteries (which uses less lithium than NCM) to lower production cost of their EVs.

So yes lithium will have to stay stable and reasonably cheap in Western markets for Western EV makers to bridge that widening gap with the Chinese.