The term "rare earth" does not mean the material is unobtainable. See
Rare earth element - Wikipedia, the free encyclopedia
Quote: "Despite their name, rare earth elements (with the exception of the radioactive promethium) are relatively plentiful in the Earth's crust, with cerium being the 25th most abundant element at 68 parts per million (similar to copper). However, because of their geochemical properties, rare earth elements are typically dispersed and not often found concentrated as rare earth minerals in economically exploitable ore deposits.[3] It was the very scarcity of these minerals (previously called "earths") that led to the term "rare earth"."
Also see
Lithium - Wikipedia, the free encyclopedia
Quote:"According to the Handbook of Lithium and Natural Calcium, "Lithium is a comparatively rare element, although it is found in many rocks and some brines, but always in very low concentrations. There are a fairly large number of both lithium mineral and brine deposits but only comparatively few of them are of actual or potential commercial value. Many are very small, others are too low in grade.""
So yes, lithium is not as common as iron and copper but it is one of the more plentiful elements. And as JRP3 posted, lithium ion batteries use only a very small amount per cell.
The size of Tesla's planned factory is due to the need for large numbers of batteries for future production, numbers greater than what is currently available.