Contrary to many scare reports, lithium is not particularly rare or expensive -- under $10 a kilogram for lithium carbonate, which is used to make a dozen or two percent of the mass of batteries that sell for hundreds of dollars per kilogram. It's a couple percent of the cost. The main risk for lithium is temporary supply shortages, where demand outgrows production rates (it takes many years to get a new mine started). And of course, everyone wants to produce the cheapest stuff, but the cheapest stuff isn't always in the best of locations (producing from seawater -- a basically boundless supply -- costs ~$30 or so per kilogram of carbonate, versus a couple dollars per kilogram from a good lithium-rich playa.
It's not batteries that will be displaced by elevated lithium prices, but the other uses, which currently make up the vast majority of lithium consumption -- alloys, greases, glass, ceramics, etc.