Design advice / help for battery low voltage cut off

A LapTop-Battery depends upon "Special-Circuitry" that is built-into the LapTop.
This makes it a poor choice for a Hobby-Project.
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Actually is a handheld console game. I'm using laptop motherboard and the original battery, much more convenient than design my own battery.
So the additional screen need to be powered by this battery.
 
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