Voltage regulator STBY & OFF - whats the difference?
These questions are usually cleared up if there is a block diagram in the datasheet. As you can see, the off/STBY pin connects to shutdown logic that shuts down everything, including the high side pmosfet switch. If the mosfet is shutdown there will be no draining of the battery. 

The LBI , Low Battery Indicator is your  logic signal created for your threshold to enable ON, hysteresis, OFF thresholds to make a decision when to go to sleep and when to wake up (like a low battery LED but that drains current).

If you want to use the LBI pin to monitor voltage, then the shutdown circuitry needs to be on (which will drain current slowly). If you want everything to be shut off when the batteries get low, then use the off\STBY with the resistor dividers in figure 3 .