Once there's a strong pipeline of electric cars headed for wreckers, the scale is there for recycling to be significantly more profitable than mining raw materials. The scale isn't there right now because most battery packs pulled from vehicles (wrecks, end-of-life, etc) are still highly valuable intact.
Companies like Redwood Materials are scaling up in preparation for this future.
(Non-vehicle lithium batteries are likely too small, too fiddily, too difficult to build a supply chain for that recycling to be economical on their own. But once the pipeline is there, adding all the small batteries to it would be a no-brainer.)
[1] https://www.sciencedirect.com/science/article/abs/pii/092134...
The only missing piece to achieving scale is a pipeline of recyclable material; this will obviously exist once electric cars begin to age out in sufficient quantity.
The dirtiest part of lithium batteries is cobalt, which is being substantially reduced (or removed entirely) from lithium battery chemistries. Lithium itself is an abundant resource and is not especially dirty, at least when compared to many other raw materials. And there are prospects for future mines being much cleaner than in the past.
With sufficient investment, lithium batteries can be highly recyclable and it's feasible that within a couple of decades, nearly all the materials in new battery production could be recycled. And would be recycled because it would be cheaper (and thus more lucrative) than mining from earth.