Why does a charging IC keep a low voltage while connected to a used battery?
It is unsafe to rapidly charge a deeply discharged li-ion battery, and so many li-ion charging chips will use a pre-set trickle charge if the battery is below a certain voltage. In the datasheet this is usually indicated by V_TRIKL and I_TRIKL.
As another safety precaution, most charging ICs will refuse to charge a battery which is lower than a certain voltage. This is called under voltage lockout. I wasn't able to find what that is for the LTH7 but I would suspect it is probably around 2.0V. In any case, I definitely would regard a 0.1V battery voltage to trigger the lockout.
One way that usually works to &quot;revive&quot; deeply discharged cells is to charge them using a constant-current power supply at a very low current. Set your power supply to 3V and the current limit to a low value like 10mA (you need a current limiting power supply). A lot of times the voltage on the cell will rapidly rise to a voltage around 3V at which point you can put it on a normal charger.