From the official nano page at https://www.arduino.cc/en/Main/ArduinoBoardNano
The Arduino Nano can be powered via the Mini-B USB connection, 6-20V unregulated external power supply (pin 30), or 5V regulated external power supply (pin 27). The power source is automatically selected to the highest voltage source.
If your Lithium battery is 6V or greater you can feed it via pin 30 and use the on-board regulator. If you have 5V or slightly less you can feed it via pin 27. Its my experience that arduino will run OK with 3 dry cells (~4.5V) fed to the +5V supply rail.
How long your battery will last depends on your application: unmodified arduino running a simple sketch will use 6-10mA of current but this can be greatly reduced with careful design and programming.