Could be an SOB buck driver. Or maybe it's a Downboy, the predecessor to the SOB. When you check the tower, see what approx diameter of driver board can fit. If it is 14mm, then that would be consistent with an SOB or Downboy. If you can actually see the driver board (presumably the non-component side), look for some small writing on the PCB that might say "SOB REV01", "DOWNBOY", or similar.
Use your DMM to do a diode check. Put the negative probe on one of the Lux V leads (doesn't matter which one). Put the positive probe on the bare tower. If the slug is electrically isolated, then your meter should not read any forward voltage. If the slug is not isolated, then your meter should read about 0.7V for Vf.
Make sure when you are powering the Lux V, you apply at least Vf+1V to run the driver (assuming it is an SOB) in regulation. That would mean Vbatt of about 7.5V min (equivalent to 2xLi-ion) for full power to the Lux V. I would think that an M6, Megallennium, or 9P would satisfy this.
Check the hookup wires from the driver to the LED. Make sure the insulation is intact, especially where the wires come out of the holes on the sides of the tower's "stem". Make sure that the solder connections to the LED legs aren't shorted to the tower.
You could de-solder the + hookup wire leg, insert your DMM in series, and measure the drive current. But if the LED isn't working right and is dim, then maybe you aren't going to measure 500mA, 750mA, or 1000mA nominal (or whatever drive current the driver is supposed to deliver) anyway.
You could de-solder both hookup wire legs and connect the driver to a known-good, heat-sinked LED, such as a Cree XR-E. If the XR-E is on a star or one of those small substrate boards, just put some thermal compound under it and stick it on some chunk of metal. Power it up briefly to see if the LED lights up brighter than the Lux V does. If so, then I'd say the Lux V is at fault. If the known-good LED is also dim, then probably the driver is at fault.