Heating and cooling, OK. Cars require batteries, and there's not enough lithium to support as many electric cars as there exist combustion engine cars now. A breaktrhough will be needed, either in battery tech or shared transportation (either public transport, car-sharing, or generalized telecommuting).
There is plenty of lithium for EV’s. Existing mines are enough for ~1 billion cars, however raw lithium is currently well under 1% of the cost of a new Tesla so vastly more expensive mining options don’t really effect the economics much. The minimal amount of recycling would change dramatically as lithium prices increase.
PS: “battery grade” lithium is more expensive, but what changes isn’t the amount of lithium but removal of minor impurities.