It really depends on the laser, and sometimes, there are even differences among the same model of lasers.
CNI lasers (Nova X-series) for example have an amazing regulation, that has a dropout voltage of only 0.39V!
In this type of laser, you will get the same power from 1.8V Lithiums as from two 1.2V Ni-MHs. 1000mAh Ni-MHs can be discharged down to 1.283V each, before the laser drops out of regulation. I am using two pairs, and charging one, while using the other.
Up untill now i thought that NewWish lasers (like DX200) have no regulation whatsoever, because i got a different current with different batteries. And measuring the current would change it.
But then i found one with an identical driver, that takes the same current from a 3V primary Lithium cell, a 3V rechargable Lithium cell or a 3.6V rechargable Li-Ion.
This means the components used are not supposed to work from such low voltages, and it really depends on tiny variances in the components from the production process, if it will regulate or not...