Regarding batteries for tennis ball machines: SLA (sealed-lad acid) are still the most practical and affordable option. Lithium batteries are very expensive and may not work with all applications.
Ultimately, battery life and effectiveness has more to do with the owner's
charging procedure than the type of battery used. Depending on the type of charger, an 18Ah lead acid battery will last 3-4 years with normal use and provide over 2 hrs of playing time on a charge. I think it's pretty unusual for any individual to use a ball machine for more than 2 hrs at a given session unless you a teaching pro.
But a battery is only as good as how it is charged. Most ball machine companies, such as Tennis Tutor, only use "smart" chargers. Smart chargers
will not overcharge the battery (one of the enemies of batteries) and make it
very convenient to recharge. If a machine is inactive for a long period and not charged, batteries will deteriorate -- another reason smart chargers are effective to prolong the life of lead acid batteries.
There is always the chance of getting a "bad" battery but that is pretty rare. So ultimately, I think the answer is to follow the charging procedures and not try and reinvent the wheel.