Overdriving LEDs makes them brighter - usually at the expense of efficincy, almost always at the expense of life.
You can drive a Lux III at 1.3A if your heatsinking solution is good enough, but most report that the only difference between 1A and 1.3A is that the emitter generates a great deal more heat. A light meter can tell the difference, but your eyes will have difficulty seeing it.
Lamina arrays are overdrivable - they're specified in such away that you need only keep the die junction temperature at a given level. The amount of heatsinking required to drive them substantially past their nominal ratings is ridiculous - hundreds of times the mass and volume of the array. Active cooling to reduce the heatsink surface area would require a substantial fraction of the power going to the array.