The tools we use now, computers, drills, etc, are often powered by batteries. Here are a couple simple articles on what is out there and what is safe. The new batteries, think Tesla, can and will catch fire or explode if mistreated. This is not a battery how to. That is a subject for serious study. It is a heads up as to what you can do to get the best use out of batteries and not blow them up. All About Batteries Li-Ion & LiPoly Batteries If you do want to go into greater detail, I like this site. Learn About Batteries Battery U has a section on life cycles of LION batteries and how the life can be 300 charge cycles or 3,000 depending on charge conditions and depth of discharge. Costs money now, in SHTF conditions, would just lose use of device. BU-808: How to Prolong Lithium-based Batteries Very good book on batteries that is on monkey. Lots of detail and gets a little over the top. Handbook of Batteries 3th edition
It appears that cycling is not as critical as other battery types, and avoiding the highs and lows maintain the health of the Li batteries.
I know LiFePo4 batts are the stuff for my portable radio ops. The discharge curve on them is perfect for that application.