I'm trying to completely discharge an LG G2 D800 with Android 4.1; however, the phone always shuts down at 2%, so it's impossible for me to go down until the absolute zero. How could I change this configuration?
This isn't a "configuration". When the phone shuts off due to low battery, the battery is completely discharged. The shutting down isn't a configuration, it's due to the battery voltage dropping too low. The fact that the battery percentage displayed is above zero is just an artefact of the way the lifetime of the battery is estimated. The displayed percentage when the battery is discharged will gradually increase over the lifetime of the battery.
So if your aim is just to discharge the battery, you've already succeeded. Try not to do this too often, as full charge-discharge cycles reduce the lifespan of the battery.