The batteries have a low voltage limit of 2.5 v. That means you should never allow the batteries to go below 2.5 v or they will be damaged and very unsafe to use. This limit is per battery.
Partly because of this limit, and for other reasons as well, regulated mods have a low voltage cutoff below which they won't fire and you'll only get a 'low battery' reading. This is usually around 3.2 volts per battery, so 3.2 volts in a dual parallel mod and 6.4* volts in a dual series mod. If your batteries are properly married, they should both discharge at around the same rate (though some differences might become detectable as they age). This means they should be at 3.1 - 3.3 when they hit the cutoff, which is well above 2.5 volts.
*The 6.4 volts in a series mod is the combined voltage the chip is receiving from both batteries. As long as the batteries are balanced, it means about 3.2 volts from each battery.