If you look at Gigafactory presentations you'll see a recycling component. Recycling obviously makes sense since they'd be dealing with a large amount of the commodities.
But there are a lot of unknowns about recycling technology, since lithium batteries are relatively young, and sometimes recycling processes lead to "downcycling", where the quality of the output isn't as good as virgin material.
Right now there's a low volume of batteries to be recycled, because people buy up salvage packs for re-use/re-purposing, volumes are low and cars are new. There's a Catch 22 that you can't have good recycling economics until you have volume, and you'll get better volume with good recycling economics.
But, on your assumption of a 10 year life, that _might_ be the automotive life. Degradation will vary. But even then, after 10 years there will, on average still be significant remaining life in the battery, which is why all of the manufacturers are looking to static energy storage as secondary use. That could allow a battery pack to be used for another 10 years. Aside from hobbyists building their own home storage, I expect secondary use to be in large commercial installations where they would have the scale and expertise to handle a more frequent hot replacement of batteries within a storage array.