General Discussion, page-589

"Solid-state battery" simply means no liquid electrolyte but a solid one for example a ceramic substance. Pretty much all solid-state batteriy programs that I know of use lithium in the cathode. In the holy grail would be to replace the graphite in the anode with lithium metal, but so far this proves to be difficult due to dendrite growth. So yes solid-state batteries will still use lithium and I have read a couple of times that the amount could increase by ca. 20 %. Joe Lowry for example mentioned this multiple times.

Here is an article that explains the components of a current lithium-ion battery: The Four Components of a Li-ion Battery (samsungsdi.com)

This could be useful as well: Solid-state battery - Wikipedia