> Your original comment said there was "23¢/kg of lithium" in waste batteries.

Yes. Is that unclear? I will try to clarify it further: my erroneous calculation was that each kilogram of batteries contained 23¢ worth of lithium, using a lithium price of US$13 per kilogram and a figure of 18 g/kg of lithium content. That would have meant that if you spent 10¢ per kg of dead batteries, you could spend 13¢ per kg of dead batteries refining the lithium from them before you ate up your profits, which would have been US$7.30 per kg of lithium produced. The corrected figures are US$1.23, US$69 (for 02019), and still 18 g/kg; if we use 50¢ we then derive 73¢ and US$41 per kg of lithium.

Does that help?

> Concentration of lithium is not the only concern

The usual term is "purity"—and purity of lithium is generally the only concern to the lithium buyer, apart from cost.

> we barely have a way to achieve this at any cost

On the contrary, the current way we have to achieve this is so incredibly cheap that an 18650 lithium-ion cell that sells for US$3 only contains 5.5¢ worth of lithium. If the price of lithium increased 1000% it would only increase the battery cost by 15%.

> If we're allowed to invoke future technology to solve this

What you are describing as "future technology" I think is probably more like "grinding up a bunch of dead batteries in a tank of water and then leaching the lithium out with some leachants". There are dozens of papers in the field that have demonstrated feasible methods; one of the simplest, from 10 years ago, used 1M sulfuric acid and 30% H₂O₂ for 2 hours at 80° with a 40% suspension of solids to leach out the cobalt (at which point drain cleaner suffices to get the lithium, I think), and another used 2M citric acid, 1.2% H₂O₂, and 60° temperature, with a 3% suspension of solids. These are processes Berzelius could have designed.

There's serious engineering work to be done, but there's no risk that it will turn out to be unprofitably hard, just because dead batteries are such a rich lithium ore.

> If we're allowed to invoke future technology to solve this, then I'm going to continue driving my ICE car, soon we will solve the problem of mass CO2 capture.

This is precisely the opposite extreme. Dead batteries are 1.8% lithium. Mined lithium brines are 0.01% to 0.2% lithium, so they're worse. When you drive your car, you mix the resulting CO₂ into the entire atmosphere, which weighs 5.15 × 10¹⁸ kg. (And into some of the oceans, too.) If you drive your car 501000 km, you've added 128 tonnes to the atmosphere. That's 0.0000000000025%. The whole CO₂ content of the atmosphere is only 0.04%.

Atmospheric carbon capture is a very difficult problem precisely because of the very low concentration of CO₂ you're trying to purify. I do think it's feasible, especially once the massive new solar energy plants come online in the 02030s, but it's pretty far in the opposite direction along the difficulty gradient from battery recycling. Also, it's unprofitable (it provides a public good), and battery recycling is profitable.

Lithium mining from batteries is easier than lithium mining from the ground because the concentration is higher. Atmospheric carbon capture is harder than lithium mining from the ground because no financing structure exists for it and because the concentration is lower.

(Or maybe the olivine stuff will pan out, I don't know. Serpentinized olivine wouldn't be very pure CO₂ but it also wouldn't be acidifying the oceans and melting the glaciers.)