In the US environmental regulations, the cost of producing power, labor costs, would all drive up the price of the end product in a way that makes it totally noncompetitive. That's also why the US and some other countries are investing in other ways to find lithium (among other things) on seabeds, where it's hoped that extraction would be less expensive. Of course the threat to the seabed environment is a concern, which in turn might drive up prices by imposing regulation, etc etc etc.
In an export model, yes. However, given their negative externalities (including geo-political factors), importing countries may place tariffs on Chinese lithium in order to make use of other sources.
If the total embodied value of lithium in any particular product is small compared to the overall value of the product, the tariff might not represent a significant drag on the indigenous industry.
It's also worth noting that Chinese prices are so low that certain tariffs can reach the stratosphere (eg: American 100% tariff on Chinese EVs), further making them unpopular with the commons.