If anyone is interested in learning more about lithium mining and battery production in general I'd recommend watching this video, likely the best Gali's video I've seen so far (sorry if it was already mentioned 100 times, can't keep up with this forum):
My thoughts are that Tesla is unlikely to go deep into mining itself and most likely will focus more on securing supplies and battery recycling instead.
Recycling, while may not sound as sexy as mining, may be a key to sustainable future and once it is mastered and enough lithium is mined, mining will be almost obsolete. Also lithium itself may be partly or completely out of equation in the future.
Still there is a clear shortage of lithium mining for the nearest future so who knows.