It's not just lithium. The more complex that electronics or other devices get, the more problems there are in separating the various pieces to produce high-quality materials that can be reused by modern industry.The recycling point is under-appreciated. For example, as companies like Apple push us away from wired devices toward wireless, battery powered devices, it's worth noting that the countries with the highest recycling rates currently recycle less than 5% of the lithium ion batteries in the waste stream.
The peak fiasco may have been the "Single Stream Recycling" concept that seemed like a good thing several years ago. The idea was that the recycling machinery could sort paper, plastics and metal into separate streams, but it was vastly overhyped. The ugly reality was that the machinery did not work well, people did not clean the recyclables well enough, and a lot of things were not as recyclable as people claimed. A few years ago, promoters were talking about recycling complex packages like juice boxes and plastics of all sizes, shapes and forms. Now it's down to clean paper, and food containers of metal, plastic or glass (but not pill bottles, shredded paper, and lots of other things that might gum up the works).
Computers and other electronics are even more complex and harder to separate and reprocess into materials that can be reused effectively.