Using a single year's supply of lithium we would be able to produce 1 terawatt hour worth of battery as an upper limit. Currently the world uses about 64 terawatt hours daily on average. Assuming we would only need storage for 1/3 of that amount, we would need roughly 20 terawatt hours of storage.
What this means is we would need to dedicate 20 years worth of current lithium mining to produce the needed batteries or expand lithium mining by a factor of 5-10 to meet climate targets.
Back of the napkin, this seems practical in the long run, but difficult in the short run. With recycling we can build up a reserve of lithium over the years, however I think it's going to take half a century just to get the lithium we need to replace fossil fuels. In the meantime we'll take a small chunk out of fossil fuel demand. However demand is still increasing.
We may want to consider subsidizing nuclear at this point to get us over the finish line on renewables. Unless we come up with another carbon neutral energy source that provides consistent power 24/7.