1. Musk is a seasoned business leader with 12+ years' experience running SpaceX and Tesla simultaneously, overseeing every aspect of the businesses, so far very successfully.
2. Clearly Musk knows he will need a large lithium supply, since Musk is not literally an idiot, which you would have to be in order to start the largest lithium battery factory in the world without thinking about lithium supply.
3. Clearly Musk investigated this matter.
4. Musk is moving forward as if lithium supply is not a problem.
5. QED, either lithium supply is not a problem, or Musk is investing billions into something that he has no plan for how to make work.
6. One of these seems more likely than the other.