This circuit maintains 1 watt load on LIPO as the battery discharges you could use a 1 Second timer to count the time it takes for the battery to become discharged which would stop the timer fully charged battery has a terminal voltage of about 4 volts adjust the input voltage to 3.2 volt the load on the battery is the same approximately 1 watt
To adjust the load change the 2 Ohm using ( 0.7/ your load current )
From the (Time Load) information you could work out how long the battery would last for other loads
Just concept need to experiment further