Lithium chemistry is very finicky. It's extremely popular because it offers some nice performance characteristics such as a high voltage and decent cost. However, the cells have very specific voltage ranges and if they ever go outside of that range, the results could be serious.
To answer your question, the voltage range of a lithium cell is between ~2.4V and 4.2V. If it ever goes below 2.4, the cell will be dead forever. If it goes too far above 4.2, then you could have a serious problem (lithium fire :X).
Lithiums love to be around 55-60%, so it's better if you don't discharge it in wide ranges. I mean, for a laser, it doesn't really matter because you're dealing with a fairly cheap battery (I buy Tenergy batts, which are generally on the higher side of the quality scale, and they are only about $10 each). But for e.g. a laptop, this actually drastically affects your battery life.
So, you don't need to worry about charging it when it's not completely empty; that's a good thing!
You also asked about how the laser behaves with respect to battery voltage. This strongly depends on the driver you're using. Because lasers behave like diodes, they should always be driven by a "current source" -- that is, they should be able to put (theoretically) any voltage across the diode with a very specific current. There are two basic ways to do this (I'm simplifying this a lot just so that you can get a good idea of what's going on): though either linear or nonlinear drivers.
The punchline is that linear regulators cannot drop a voltage across the diode higher than the voltage of the battery minus some dropout voltage that the regulator requires. A nonlinear regulator will allow you to output a much wider array of voltages so that even if your battery drops down to say 2.8V, you could still drop 3V across the diode.
Most cheap lasers like the ones from O-Like use linear regulators. That means that when the battery is about 3V, your laser will cut out. You might be lucky and have something with a boost regulator, though. The first laser I ever bought had a boost driver and runs fine on NiMH cells.
