biggest thing with lithium, and you will see this in the R/C world, and why your power tools abruptly stop is, its not that the battery goes dead and stops. lithium batteries are so "active" that it is very dangerous to charge a lithium battery that is completely dead. where your 12v Deep cycle battery can be ran all the way down, a lipo cell (1s) has a charged voltage of 3.7v (man i hope im remembering these numbers correctly) and is done at 3.3v while that doesnt seem like a lot, the WHOLE useful life is within that .4v when lipo's drop below that voltage (3.3v per cell) they become very unstable when charging and thats when they can catch fire. most r/c cars have a low voltage alarm, or the electronic speed controller will cut the power way back enough for you to drive the vehicle back to you and thats about it, and thats why your power tools just stop. that is their low voltage alarm.
please correct me if i am wrong on any of this. i has been a while.