Building enough battery capacity for the grid would be far more than current world demand for Li-ion cells. I imagine prices would skyrocket, throwing off your calculations.
Short-term storage isn't that bad, we have other battery chemistries or even completely different types (e.g. flow batteries). A bigger problem is seasonal storage, for which most batteries are far too expensive.
For grid storage I think molten metal makes the most sense. It's a technology that was developed to be ideal for grid storage from the start. Flow cell batteries might also make sense. And then there's other storage technologies like compressed air, pumped hydro, storing kinetic energy, storing thermal energy, etc.
http://news.mit.edu/2016/battery-molten-metals-0112 https://www.youtube.com/watch?v=NiRrvxjrJ1U
But that's only one of many energy storage technologies that can be used for batteries. It's popular for mobile/portable uses because it has high energy density, but that's not really necessary for grid-scale energy storage; whatever's cheapest will do (which may well be pumping water uphill).
Most of the lithium found today is extracted from brine reservoirs located in regions of southwestern South America and China.