After using my camera for about one year, it would turn off rather quickly with a low battery indication. So I switched to the second lithium battery that came originally with the camera. But I'm having the same problem with the new battery. Now I'm wondering if this second battery aged from just being in the box. Any advice would be helpful. Also, where can I buy new lithium batteries.

All batteries exhibit decay, or, spontaneous discharge, at different rates according to their construction so the second battery could well be unusable. The problem with the Lithium structure is that it is not possible to test how much capacity remains in a cell. Even “discharged” cells will often measure 3 volts on a voltmeter but have no actual usable capacity left. This is due to the chemical way that lithium batteries work.