Lumens factory are giving you correct numbers!
The rated voltage of any lamp is nominal. You can stick any number of different voltages through it, from under driving it to verging on making it go
.
It is listed as a 12v lamp because it is designed to run in the M4, so nominally it is a 12v lamp (4 x 3v CR1232s).
However....battery manufacturers take the voltage sag when under load into account when designing their bulbs to get the best performance from them.
Under the 2.15a load from this lamp, the voltage from 4xCR123s will sag quite a bit (apparently to about 9.2V!), LF have obviously determined that they can use a 9.2v lamp that draws 2.15a with 4xcr123s, because under that load the cells are putting out about that voltage. LF lamp may well be driven quite hard, but this is what makes it nice and white.
The fact that 3x RCR123s (about 12.3v to 12.6v off the charger) doesn't make it go
is also evidence of the voltage sag when under load. And not good evidence either! That the 12.3v is sagging sufficiently not to instaflash the lamp indicates the cells are being driven awfully hard. Either that or it's an indication that one of the cells is stuffed, which is a possibility and even more worrying.