The standard countryside yokel reply when asked for directions applies, " Arrh, If you need to get to there, I wouldn't be starting from here".
For battery powered LED lighting - you shouldn't be using 12v LED strips. You should be using bare LEDs and a constant current supply. Converting cell voltage to 12v, only to use (probably) resistors to limit LED current isn't the way to go.
You will lose far more, efficiency wise, starting from there, than you are worrying about losing in the series or parallel considerations.
But then, you'd design the required power source and then the charger associated with it - not start with a charger, which then constrains your battery pack topology.