Old lead battery are highly recyclable but AFAIK the type used in EV's (and in many electronic devices such as laptops and phones) such as Li-Ion are not (easily) recyclable right now.
Hopefully by the time discarded batteries will increase in number there will be solutions, but right now there are only some "pilot" plants/technologies, see:
It is not particularly economical to recycle EV batteries yet because they're still worth a lot more on the secondary market for non-mobile use. When we have a surplus of them, it will be cheaper to reclaim the lithium from the old batteries than it is to mine new lithium.
