Okay, several things.
First, car batteries are the single most heavily recycled object on Earth, bar none. Now, that's largely because they're lead-acid, and the economics works out much better for recycling PbA. But part of the reason why recycling li-ion isn't more profitable is that because... wait for it...
*Lithium is cheap*
Lithium carbonate, the primary form lithium is traded in, generally costs $4-8 per kilogram. That's dirt cheap. That's why we can get away with using it in cheap products like lithium greases and glasses. Nissan has publicly stated that the Leaf contains 4kg of lithium metal equivalent. That's something like lower-20s (too lazy to do the math right now) kilograms of carbonate, or just over $100 or so worth of carbonate. In short, a virtually insignificant fraction of the price of the vehicle. The price could double. It could triple. It could 10x, and you'd still barely notice it.
Reserves figures are for *current technology* at *the current price point*. Change either of those two factors and the scale of reserves figures radically changes**. For example, if lithium prices rise to somewhere in the $20-$35/kg range, it becomes economical to extract lithium from seawater -- and the amount of lithium in seawater is virtually limitless. Even at the upper end of the current range, huge new reserves are starting to come online. For example, the Kings Valley, Nevada isn't factored into current reserves figures, yet there's a new mine being built there by Western Lithium Corp. They've decided that tech has advanced enough and the price point is high enough that it's now profitable. That deposit alone nearly has as much lithium as the entire current "reserves" figure for the world combined.
There is, and will always be, scaremongering about various resources. Occasionally, it's even valid. But in the case of lithium, it absolutely is not. The primary risk for lithium is about scaling -- that is, whether production of EV batteries requires an increase in global lithium production faster than we can develop new mines and processing plants to produce it.