Typically when a lithium-ion battery is recycled some metal parts are extracted (the battery contains metal plates which are relatively easily separated), but the lithium usually is not as it’s a lot more complicated to extract. Economically it is a lot cheaper just to mine new lithium, so proper recycling facilities don’t often exist.

In the U.K. lithium-ion batteries are usually discarded in a landfill, and often treated as hazardous waste:

https://app.croneri.co.uk/feature-articles/dealing-waste-lit...