Oh, that was yours
I'd like to have a high power DPSS in something that size too, but I'd put a 3 inch diameter PCX lens on the end of it for uber low divergence
I don't know what is required to run most labbys, or this one. I'd make the supply voltage high enough so the voltage doesn't drop too far to run the laser too early, i.e., as an arbitrary example; if you needed each cell to be 3.8 VDC to produce enough voltage in series, the laser would stop working before the batteries are depleted much.
I'd need to know the current and voltage needed to give a better example or opinion. Last time I gave an opinion on batteries I was misunderstood due to the minimum voltage needed to run the green laser diode, then challenged and whipped with a wet noodle, so I'm going to be more cautious this time around and state a disclaimer; the voltage a Li-ion battery is depleted so far it should have a recharge can vary quite a bit by manufacture and model of battery, regardless of the size. Instead of using batteries like that, I'd look into using a Li-ion brick.