Dont run the batteries dead. I have used Lithium ion packs in a different application. They work great but there is a stop load voltage of about 3.45 volts per cell under a 1 amp load on the cells I use. If you run it below this you risk damaging the cells. If you run it dead it is toast. Find out the operation limits of the cells you are going to use.
questions: How many Mah are the cells rated for?
What is the pack voltage?
Is there a charge safe circuit built into the pack?
How are you planning to charge them?
Fitz