I have a type S brand jump starter pack that I bought a couple of years ago at Costco.
When you connect it, it MUST read voltage from the battery or it will continue to blink and state "Connect cables to battery" I don't know how low the voltage can be, but it will work at 4.5 volts.
The first time I used it, it was for my lawn mower. Unfortunately one of the battery cables was loose, and didn't make a good connection. When I connected the jump starter, it didn't read enough voltage and kept displaying the above message. It didn't send power to the mower and it didn't start. After I tightened the cables, it worked fine.
Last year at 5AM I went to move my daughter's car in the driveway so we could pack it up for a trip to Florida, and the battery was dead. I used the jump starter, and it worked beautifully. We decided to keep the engine running even when getting gas so as not to need to rely on the jump starter again.
When we got to our destination, I bought a new battery. Thankfully it wasn't a failed alternator.
A couple of weeks ago, my rear windshield defroster stayed on and killed my car's battery. This little battery pack started my 4.6L small 8 cyl, without a problem.
It's a lithium battery pack and has held a charge at 95% for a year at a time. I'm pleased with it. It would be better if it would start an engine without a battery connected though.