Earlier quoted context omitted.
We will never run out. Lithium is infinitely recyclable, is common in underground brines and some rocks all over the world, and has sufficient concentration in seawater that it can usefully be extracted (for non-insane cost) if for whatever reason all other sources are exhausted.
Correct. Certain kinds of lithium batteries can be limited by the availability of other elements used in them, which are less abundant than Li, e.g. cobalt. There are efforts to reduce or eliminate the use of such elements.
So there are lots of alternative batter chemistries that all have lithium as the common element.