Hard rock lithium -pegmatites- were actually the majority of global lithium until recently. They were/are primarily used in ceramics. Brine-produced lithium has one fewer step to convert to lithium in batteries, but the cost is absolutely marginal. These pegmatites are common worldwide, unlike brine deposits.

Brines are mined somewhat like fracking- a borehole is drilled and water (without fracturing compounds) is injected and then pumped out into large evaporating pools, leaving behind lithium-containing salts. It's extraordinarily cheap because it's dead simple to purify and doesn't even involve actual mining. However these sites are uncommon (though there are still several in the US, and worldwide- they are not limited to South America) and since you're limited to land area, evaporation speed and water supply, this is a limited and slow process. And the water use can be a real problem- brines often exist in places with limited water supplies as the water washes the lithium away over long timescales. Still, the evaporation pools often support life for a time, and flamingos like them. It would be much better to not waste the water though.

Hectorite is the main focus of this article. It requires a couple more steps (limestone roast and acid leach) to extract and costs ~$2/lb[1] (NB that was in 1987) compared to current carbonate prices of $2.5-$3.5. I wouldn't say it's nonviable because it probably helps to put a ceiling on the long-term price of lithium, however high lithium content in these clays is .35-.65% compared to 6%+ in pegmatites. I'm not sure it will ever be relevant. Also note that although "acid wash" sounds bad, it doesn't have to be. The acids get reused.

The bottom line is that lithium is highly available. It contributes very little (<5%) to the cost of a battery, so huge disruptions (4x price increases in the last lithium shortage) have very little impact on the price of batteries as long as availability is not affected.

The biggest price factor in most batteries is cobalt- it's very expensive and makes up many times more of a battery's mass than lithium. Currently most of it comes from two countries in Africa. The DRC is one of the few places in the world where cobalt can be found on its own. Despite this it's almost always found with nickel, which is produced in huge quantities. For the moment the cobalt supply for batteries will remain stable solely because of the recovery of nickel prices- this has caused a half dozen or so mines to open/reopen in the US. There was a strong fear that cobalt would put a brutal penalty on the price of lithium batteries during the nickel price crash, and eventually that might still be the case. It's also worth noting that there are many alternate chemistries that don't use cobalt, but the best ones do. It's possible that a new chemistry (such as li-metal/foil batteries) may change that, but unlikely.

Finally, graphite is the last supply threat. Battery graphite is about a 40/60 synthetic/natural blend- both types have advantages and disadvantages, so they are used together. High quality spheroidal graphite is hard to find, but the synthetic stuff is nearly as cheap so it's unlikely it'll be a problem. I don't know much about the specifics but I think it comes down to a lack of searching, ie it's easier to sell high quality graphite as anthracite coal than to worry about selling to battery producers.

[1]: http://digicoll.manoa.hawaii.edu/techreports/PDF/USBM-691.pd...