Thought the same thing with the laptop batteries...So the disection commenced. A very wide and long strip was obtained. (Actually, two strips of unknown identity).
Well, if it was a Li-ion battery then neither of the strips was pure lithium metal.
In Li-ion batteries the lithium is stored in "intercalated" form - interspersed with carbon atoms in a sort of crystal. I suppose that in a charged Li-ion battery that this intercalated lithium might be available for use in a Birch.
This first URL requires a Postscript Document Viewer:
http://www.panasonic.com/industrial/battery/oem/images/pdf/li-ionoverview.pdf (http://www.panasonic.com/industrial/battery/oem/images/pdf/li-ionoverview.pdf)
The parent URL of the above:
http://www.panasonic.com/industrial/battery/oem/chem/lithion/ (http://www.panasonic.com/industrial/battery/oem/chem/lithion/)