Right now there are both articles about how lithium mining is terrible and expensive (https://www.wired.co.uk/article/lithium-batteries-environmen... "The spiralling environmental cost of our lithium battery addiction"†) and articles like this one about how we're producing a massive waste stream containing high concentrations of valuable metals like lithium, cobalt, and manganese. (A 2600-mAh 18650 cell contains about 800 mg of lithium, and https://lygte-info.dk/review/batteries2012/Aosibo%20IMR18650... says it weighs 45 g, so it's 1.78% lithium by weight, 35 times as concentrated as the brine. At US$13k/tonne that's about 1¢ of lithium per battery.)
People throwing out valuable metals while other people are spending a lot of money to recover those same valuable metals from highly diluted deposits? This sounds like a case for... capitalism!
(This is completely different from the old battery waste problem, where mercury was included in disposable battery electrodes in order to stabilize the battery chemistry, which is a serious toxicity hazard and a real pain in the ass to separate out. That's never been the case with lithium batteries and has even been eliminated from almost all disposable batteries now.)
As pointed out in https://xkcd.com/808/, if dowsing could tell you what was under the ground, companies would be using it to make a killing in oil prospecting. If casting hexes on your enemies worked, companies would be using it to make a killing in... killing. Military contracting. (Actually, probably military leaders would.) And, when there's a significant waste stream of lithium batteries available, companies are going to make a killing by buying up these used lithium batteries for 10¢/kg and extracting 23¢/kg of lithium from them.
Until then, it's not a problem.
Unless somehow modern capitalism is failing to be ruthlessly profit-focused enough.
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† The Wired article says "500,000 gallons [of water] per tonne of lithium", which, in non-historical-re-enactment units, is 1.9 million liters per tonne, but probably more accurately 2 million liters. That puts the lithium content of the brine at 0.05%.