Why? There's not much difference in voltage, and all of these 2x123 lights are operating with a battery voltage higher than the forward voltage of the emitter, and using a buck circuit. Some of them do have a high limit on voltage, and low levels can be brighter with Li-ions because some achieve those levels by using resistors that make current output dependant on input voltage, but all you have to do is measure the wattage at each level with primaries and rechargeables(and see if it changes significantly) to know if your light is regulating with whatever batteries you're trying. There is no reason using Li-ions will lessen emitter life unless they are overpowering and/or bypassing the circuit, so that the light goes into direct drive. This is usually an issue with single cell lights that use a boost circuit. It's possible for them to damage the circuit by exceeding its voltage limit in a multiple cell light, but this really shouldn't be a problem with your Tenergy cells. Something to beware of when trying 3.7V Li-ions, though.
There has always been controversy over using the E2DL with 2x3.7V cells, but I've used AW's protected 3.7V nominal R123s for a couple of years with the E2DL for ~1hr. per night with no ill effects. I do use 17670s with my E2L because the low level was affected with the AW cells at full charge, though.
I don't see why you would have any issues with the 3.0V Li-ions in either of your lights. We're talking <1V of difference between a pair of fully charged 3.0V Li-ions and a pair of fresh CR123As.
Thanks for the opportunity to lapse into flashlight geek lingo...I'm in the middle of a 2 year break before replacing my current stuff.
Keeping up with the latest in emitter and battery technology was getting impractical...if it ever was practical
Unless runtime is an issue, I'd stick with those Tenergy cells until they go bad. If you have 16, might as well get your use from them. They'll have to be replaced after a few years of regular use, anyway. Several of my 3.7V Li-ions are on the verge of kicking the bucket due to heavy use, but I'm going to kill them all before buying a new batch-by then, newer lights might completely change my battery setups, and I don't want to be left with a bunch of rechargeable cells that are just sitting there.