You'll get tons of opinions on how far down you can discharge a lithium battery. The most common worry is that you will shorten the battery's life or reduce the battery capacity if you take it down to 0% often. I have only once run my two lithium batteries to 0%, and that was an accident.
I can only speak for Battleborn batteries, as that's what I have and have researched. The manufacturer says:
Will I damage my battery if I bring it down to 0%?
No, you will not damage the battery. We do however recommend that you put devices in your system to cut the voltage discharge on your battery at 11.5V for convenience. Our BMS system prevents the battery cell from being damaged in the event you do discharge to 0.
A Battleborn battery is 10 volts at 0% capacity when it shuts itself off. They also say you have 5 days to recharge the battery when it shuts off at 10 volts. If you don't recharge it within 5 days, it will be damaged and void the warranty.
Oh, and when they say to "put devices in your system to cut the voltage discharge on your battery at 11.5V for convenience", that's about 5% charged.