the lithium AA and AAA cells are about 1.8V fresh and new, and can maintain a good 1.6V under a load, although they could be still concidered a 1.5V type of cell they are not much like thier carbon and alkaline counterparts.
The usual alkaline cell might start at a max of about 1.68 (ever, more like ~1.6) and sags quite a bit in voltage. Some lights and devices are designed with that alkaline voltage sag in mind, it is especially important with 3XAA and 3XAAA items with direct drive and direct drive with PWM, them 3Xs you can ruin. With this low drive light a single primary 1.5V type lithium cell should not be a problem ever.
The Li-ION (lithium rechargable) cells , the 10440 type cells that people will stuff into AAA flashlights would be 4.2V and could easily ruin lots of lights it might be stuffed into. That would be a problem. mabey they are afraid if they mention lithium somone will stuff a 3X voltage battery into thier light and ruin it?
The only other "problem" is although the lithium cells are powerhouses of output , the consumer energyser type is not designed for very high output, hotwires and extreeme current, I cannot see where that would apply at all to this light item.
http://www.candlepowerforums.com/vb/showthread.php?361316-Glo-Toob-AAA-now-out
Conclusion: I would use that item with a 1.5V type standard energyser lithium primary cell, without a worry, I would want a clarification when they say NO, seems rediculous in this case.
There are "boost" type curcuits that work like simple voltage multiplyers , just raw doubling the voltage they get from the battery, I have only seen such curcuits used one time, it would be very rare to apply a curcuit like that. Also there is the sloppy curcuit, that leans quite a bit as the voltage changes. Something like that the voltage can follow the battery voltage some, and it would usually be noticed as a increase in output with the usual voltage sensitivity of the led the output would change lots. there is no indication of that from the user information either.
