Why do you think Lithium is running out? There is enough Lithium that could be mined if there was enough political will (and sometimes price signals).

Besides, we might also use other battery types, such as Redox-Flow for long term storage.

The current "backup" plan is to produce Hydrogen or P2G continuously, store it, and use it in cheap, inefficient gas turbines for the week every few years (without large grid interconnectivity) where there is a prolonged Dunkelflaute.