Hi maxa beam,
The term lithium is very general and could mean many things..
I assume you are talking about protected lithium cobalt cells.
with that assumption....
Lithium Cobalt cells are in their most natural state, where they are suffering from the least internal breakdown when at about 3.9V (+/- 0.1V). Anytime the cell voltage is lower or higher than this, the rate of wear is slightly higher, but it very acceptable within certain ranges. From ~3.5-4.20V open circuit, the cell is still in what would be a totally safe operating range.
Pushing the cell out of this boundary, like discharging to 3.0V open circuit or lower, or overcharging to 4.30V or higher, will speed up the aging process. The further "out of bounds" the cell goes, and the longer time it spends there, the more rapid the breakdown.
The protection circuit on a LiCo cell will generally kick in at ~2.5-2.75V depending on the brand of cell and which PCB is used. But keep in mind, that the load on the cell drags down the voltage temporarily, and when the load is removed, the voltage rebounds. When a cell is under a reasonably significant load (like say 1C give or take), and the PCB terminates the discharge at 2.5V, but the cell then rebounds to over 3V open circuit. So the cell only spends a few moments at the end of the discharge below 3V, which is really where the major wear and tear begins for this cell chemistry. Spending the last 30 seconds of a discharge in this range isn't too big of a deal, but isn't exactly great for a cell either. What's really hard on protected cells, is configurations that very slowly drain a LiCo cell down to that 2.5V as the last drops of stored energy are squeezed out, but slowly enough that it doesn't trip the PCB until the cell has spent a long time below 3V delivering power, and in these cases, the cell voltage will usually not rebound above 3V, it'll be like 2.7-2.8V after the discharge is terminated.... If you are out and about doing something, then it's possible that the cell may be then rested in a state of over-discharge (<3V) for hours or days, which will likely take a toll on the health of the cell...
Usually, a few incidences of slight over-discharge on a protected cell is no big deal, and if you can pop it back on the charger quickly so it spends very little time stored like that, then the cell will hardly know anything was wrong. The problem can crop up if the cell is repeatedly discharged like that, or stored like that, for months or years. This is likely to result in a cell that does not take a charge properly, and has an increased risk of vent--with-flame during charging.
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Ok, that may have been a little lengthy, but helps get the point across... think of the protection there as something to prevents the cell from being discharged to state where serious aging happens quickly. You're best off trying to recharge the cell when it reaches around 3.7V open circuit, or about 80% discharged. But you can top off a LiCo at any time if you wish
Eric