Safe and stable discharge rate for Li-Ion battery packs
You did not mention the voltage.  What you need is the battery's discharge rate. How many amps per hour.  Lithium ion usually charge at 0.8 of discharge rate.

Charge and discharge rates of a battery are governed by C-rates. The capacity of a battery is commonly rated at 1C, meaning that a fully charged battery rated at 1Ah should provide 1A for one hour. The same battery discharging at 0.5C should provide 500mA for two hours, and at 2C it delivers 2A for 30 minutes. Theoretically. Faster discharge rates will diminish the rated capacity.  

If the battery gets too warm then you need to reduce the charge rate.

The advised charge rate of a Lithium  Energy Cell is between 0.5C and 1C; the complete charge time is about 2–3 hours. Manufacturers of these cells recommend charging at 0.8C or less to prolong battery life; however, most Power Cells can take a higher charge C-rate with little stress. Charge efficiency is about 99 percent and the cell remains cool during charge.

Some battery chemistries can take more than a 1C charge.

Lithium Manganese Oxide 3C max
Lithium Titanate: 5C max

These should be charged a .7C - 1C, may be able to go over 1C, check temperature.
Lithium Iron Phosphate
Lithium Nickel Manganese Cobalt Oxide 


These do not exceed 1C.  .7C-1C recommended.
Lithium Cobalt Oxide above 1C shortens battery life.
Lithium Nickel Cobalt Aluminum Oxide, above 1C shortens battery life.


If you drain the battery to zero you will be significantly reducing the number of charge cycles.