I've lived in a world of batteries for reasons I won't bore you with.
Battery University is a site I place faith in.
Here are some important quotes for you to keep in mind;
Lithium-ion is a very clean system and does not need priming as nickel-based batteries do. The 1st charge is no different to the 5th or the 50th charge. Stickers instructing to charge the battery for 8 hours or more for the first time may be a leftover from the nickel battery days.
I try to never allow my battery to get so low that it shuts itself off and here is why;
Extreme low voltage must also be prevented. The safety circuit is designed to cut off the current path if the battery is inadvertently discharged below 2.50V/cell. At this voltage, most circuits render the battery unserviceable and a recharge on a regular charger is not possible.
There are several safeguards to prevent excessive discharge. The equipment protects the battery by cutting off when the cell reaches 2.7 to 3.0V/cell. Battery manufacturers ship the batteries with a 40% charge to allow some self-discharge during storage. Advanced batteries contain a wake-up feature in which the protection circuit only starts to draw current after the battery has been activated with a brief charge. This allows prolonged storage.
In spite of these preventive measures, over-discharge does occur. Advanced battery analyzers (Cadex C7000 series) feature a 'boost' function that provides a gentle charge current to activate the safety circuit and re-energize the cells if discharged too deeply. A full charge and analysis follows.