Not sure if you've ever tried to vape with a battery that is run down to 2.7 volts...but it's near impossible or unpleasant. I don't think there should be any concern of over discharging the battery, unless your persistent on trying to make use of the poor and minimal vapor produced at less than 2.7volts.
Getting the battery down to 2.5v is even harder. I've tried this on my
mods...not fun. Once it's at a steady 2.5 or lower, it's not likely you'll be able to recharge it through a smart charger or conventional methods. It will require a high voltage charger and cycling the charge...alot of work and dangerous.
The most important thing to have is a smart charger so that the battery isn't over charged.