Hi Duncan
5.2 LPM is the maximum possible flow rate of the pump in perfect conditions. In reality the actual flow rate will be lower. Even at the pump outlet It is unlikely the pump will produce the maximum stated flow rate.
Battery state can have an impact if the battery voltage is very low and is struggling to provide sufficient current as demanded by the pump.
A controller will adjust the pump speed as required, if you have the control set to max then the pump will be run very close to its maximum potential.