Production of lithium from hard rock isn't very different from lead, and lithium production from brine is far easier.
Hard rock lithium is most commonly extracted in the form of spodumene which is about 6-7%[1] (8% when totally pure) lithium oxide. Rich lead ore may have 3-8% lead content. Obviously comparing the two is difficult since lead is about 20x denser, but they're on the same order of magnitude. As a ratio of rock in to metal out by volume there is probably a bit more lithium, but by mass lead ore is probably 2-3x more concentrated.
For both lead and spodumene, the ore is crushed, separated by density, ground, counditioned (treated with acid to remove organics/slime), froth float separated, cleaned, filtered and dried[2]. That gives you metal that is ready to be reduced in a furnace (or electrolytically or chemically, for lithium). Both processes use the exact same machinery and chemicals (sulfuric and hydroflouric acid, and NaOH). Both processes are almost identical except that the lithium is collected at the low-density end and lead is collected at the high-density end.
Brine production is much easier and involves a well, a pump, a bulldozer and a bunch of sodium carbonate (water softener)[3]. It is significantly cheaper than any other metal production method, as well as low-energy, low-waste and low-impact. The only downside is there is a lot of water loss to evaporation. It's a relatively small amount of water, especially compared to a farm of the same size, but brine mines exist exclusively in places without much water to start with (otherwise the brine would have washed into the ocean already). It's a tradeoff.
Regardless, the difficulty in producing lithium is most certainly not most of the price difference. First, annual global lithium production is ~36,000 tonnes vs 5 million tonnes for lead, a 140x difference. Lithium's lower density could account for a 2-3x price per tonne difference, but it is vastly more likely that economies of scale are the culprit.
Not only that, but the current lithium price surge is entirely due to market contraction. It takes 2-3 years to build a mine, and longer to decide to build one. Tesla wrecked the battery market in less than two years, becoming the largest battery consumer. There simply hasn't been time to open new mines yet. The prices will drop as soon as they catch up.
Finally, the majority of lead is produced by recycling. That 5 million tonnes mined each year is less than 50% of all lead. The recycling industry obviously drops the price of lead immensely, and lithium will take advantage of recycling too, when and if it ever needs to.
>But statements like this should really be talking about the "economically extractable ore"
There is no such thing, really. Not even for oil. The content of the ground is not mapped that well. As soon as people go looking for lithium, the reserves will skyrocket just like they did with oil. Trust the crustal content more than the global reserves. Lithium is so cheap and ubiquitous that nobody has gone looking for it since the 50s- Seriously, that's the last time the USGS did a survey of US lithium supplies.
>I'm much more worried about rare earths.
Don't be. They're only used in hybrid cars (neodymium) and even then they aren't needed. You don't need magnets to make a motor, just steel and copper. The other green use for rare earths (tellurium) is in thin-film solar panels, which make up 5% of all solar panel production. Rare earth elements aren't even the first choice for these technologies, and a contraction in supply will push them out of favor entirely. Seriously, the only reason we use thin-film solar is because it's cheap, even though it's less efficient. If it's not cheap, then we won't use it at all. Good riddance.
[1]: http://encyclopedia2.thefreedictionary.com/Lithium+Ores
[2]: https://www.911metallurgist.com/blog/froth-flotation-spodume...
[3]: https://www.thebalance.com/lithium-production-2340123