From what I have read of both technologies, the LRT only increases surface brightness by reflecting light back onto the die of the LED. This of course makes the die increase in both brightness and probably heat too. When the light is then passed through an optic it is brighter by 40% compared to just an optic (like an aspheric) if you were to measure the LRT output and a good TIR optic in an integrating sphere, the light outputs would be very much the same OTF since the LRT doesn't allow wasted light to soak into the black space between the LED and the Aspheric. Similarly, a TIR (or even a reflector) can get most of the light out the front relatively efficiently.
The DEFT works better still. Instead of reflecting light back onto itself, which in my opinion only collects the scatter and puts it back onto itself, the DEFT pre-collimates the light and then sends it through an aspheric. This is much more efficient for a throwing style light.
Basic run down for throwers.
Reflector: reflects light from the LED out the front. Any light not collected by the reflector is spill light, which while it can throw relatively good, any spill light is not thrown forward, and considered lost. Small die LED's work good with all reflectors, Large LED's require larger reflectors to throw at all.
Aspheric: focuses light through an optic and collimates the beam so it is all throw. The light escaping from the LED to the sides, usually gets soaked up in the head of the light between the LED and the lens.
Reflex: Has the LED on the front glass facing backwards into the reflector. Less spill, and more throw than a reflector, more efficient than aspheric, but limited due to cooling of the LED
TIR: Total Internal Reflection... or something. Basically, all light reflects, refracts within the optic, and pushed out the front. Much tighter beams can be achieved than reflectors, with much less light lost as spill or soaked into the optic itself.
LRT: As mentioned above, creates higher surface brightness, can be coupled with aspheric, less loss as spill, but light still lost between die and lens. Higher surface brightness also probably means much higher temperatures at the LED, so better have very good heatsink. I don't think this is as good as TIR or reflector for total light output, but would be better than straight aspheric lens
DEFT: pre-collimates light before sending light through aspheric. Not sure exactly how it works, but is better than LRT and straight aspheric. From beamshots... is all throw and pretty much nothing else.