The concerns are building new mines and extraction plants fast enough to meet during demand, and the environmental damage from doing so. There are no concerns about running out.
You use something like Starship to deliver construction equipment that can be used to build engines on the asteroid it to earth orbit for processing.
Ideally you'd bring the minimum amount of equipment necessary to do in-situ production of the rest of the equipment, but we're not at that boot-strap self-replicating level quite yet.
Or the fuel required to get the fuel you need to the asteroid.
Fuel that has to be lifted into orbit. Which requires fuel.
Go look up the costs of lifting equipment just into orbit. Then look at how much lithium is worth per kg.
Then go look at the fact that we have exactly zero manufacturing capacity in space. Simple operations and repairs using pre-made parts on the ISS take hours-long spacewalks that require weeks of planning. And you think we can "build engines" on asteroids?
This is also why things like gold or platinum are good to mine from asteroids, because they have not had the opportunity to sink to the core of those asteroids like they did on Earth. (And getting to the core of an asteroid is a significantly more reasonable proposition than getting to the core of the earth)
These guys look like they have some promising technology: https://energyx.com/ They are currently testing membranes that can selectively let through lithium. Their solution vastly reduces cost, water usage, and energy usage.
The problem with lithium is that it is spread out, that means you can't really find good ores with high concentration.
Additionally, lithium behaves less like copper, nickel and so on, and more like a specialty chemical.
Mining lithium is basically more running a chemical plan and only very few companies can do it so far.
This leads to a situation where lithium mines are very hard to make profitable and you need a huge amount of knowledge to run one. The on-boarding of new mines and expansion of capacity is the problem, not the total availability.
This article* talks about enough for 3 billion EV's, depleting supply in 2100-something.
* https://www.pv-magazine.com/2020/09/15/how-long-will-the-lit...
Lithium price has gone up a lot because demand is growing faster than the mines and plants that extract it. That 80 million tonne figure was based on low prices -- at high prices a lot more reservess become viable and we have a lot more.
Also, batteries more suited to grid-scale operation like iron-flow are already in commercial use and will likely replace a fair bit of the large-scale lithium ion battery market.
Lithium ion batteries use a zeolite cathode which have atomic sized pores that safely 'stores' the metallic lithium[1]. Issue with sodium is unlike lithium sodium increases in size when reduced. That tends to damage the cathode.
For ion batteries the cathode is the big technological challenge. Has to be cheap, manufacturable, stable, conductive, and hold as high a percentage of lithium as possible.
[1] There are lithium batteries with bulk lithium cathodes. But they are hazardous.