The low-battery circuit is powered by a 3.7 V (nominal) lithium ion battery with graphite anode.
The different degrees of functionality (checkmark represents the functions seen in this version of the project):
The battery cannot be allowed to fall below about 2.4V, or an internal chemical reaction will occur where one of the battery electrodes can oxidize (corrode) through a process which cannot be reversed by recharging. If this occurs, battery capacity will be lost (and the cell may be completely destroyed).
It is important to note that Li-Ion cells will not tolerate trickle charging at all after they are fully charged. If current is continuously forced into a fully-charged Li-Ion cell (even a very minute current) the cell will be damaged. For this reason, Li-Ion cells are charged using constant-voltage (C-V) chargers, and not constant-current (C-C) chargers.
Batteries are acutely sensitive to operating temperature with respect to their charging characteristics and A-hr capacity. Most well-designed chargers have temperature sensors to assure that the battery temperature is within the allowable "window" for charging (if not, the charger will not turn on the current source). The Li-Ion cell (as advertised by the few manufacturers presently making it) can be safely charged at temperatures between 0-45°C. The operating temperature range during discharge is specified as -20 to 60°C.