I think the Astrolux S1/BLF A6 will do that with a 16340.
These lights use 18350 Li-ion, not 16340. I run mine on Keeppower IMR 18350, and its output is pretty good. Although I am not able to measure lumens myself, I have read reports from others who measure over 900 lumens. DBCust got 986 lumens on Efest purple 18350.
Sure a factor will be the cr123a struggles over 1.5a as well.
That's what I have read, too. CR123A is rated by most battery manufacturers for a maximum continuous discharge of 1.5 amps. Voltage sags badly above that.
CR123A were great for the incandescent flashlights SureFire was building twenty-five years ago. Frankly, however, they cannot supply enough current for modern, high-power flashlights. They have a place in the flashlight world, but not in applications where you are pulling 3 amps to generate 1000 lumens.
Their small size, long storage life, and good performance at both low and high temperatures mean that CR123A batteries will be around for a long time. Just don't expect high output.
The
Olight S1 is a good example. In Turbo mode, it pulls over 2 amps from a CR123A battery in order to produce a nominal 500 lumens. But that doesn't last. The S1 has a timed step-down at 90 seconds that reduces output to 50%.
Notice I said, "nominal." If lumens, battery voltage, and battery amperage were measured during this 90-second run, I suspect that they would reveal a battery that was struggling to keep up. I believe the S1 uses a boost driver. If true, then it would demand increasing current as the voltage sagged. That's going to be nearly impossible for CR123A.