Those lithium batteries use LiFeCO4 (lithium-iron) chemistry and has much, much higher output current than lithium-cobalt batteries used in laptops. They don't have thermal-runaway issues laptop batteries have either. However, for size, they have less capacity.
Along with most of them not having over-discharge protection means you can run them down very quickly. I used one on my race-bike for years without any issues. One great benefit is no self-discharge like lead-acid batteries. I left it over winter out in cold and 6-months later, it started up bike just fine!
Then I got similar lithium battery for race-bike and moved old lithium to street bike. However, one time I parked in driveway and walked down to get mail. Talked to neighbor for 5-10 minutes max. When I came back, I found I had left headlights ON! Drained battery down past recharge point. It was dead, pakut! Couldn't charge it back up.
I've been searching for lithium battery that has over-discharge protection and it doesn't appear anyone makes one. I'll just add an external cut-off circuit that'll disconnect battery when it drops to critically low voltage.