3 watt LED plus LiFePO4 battery (1 cell), no resistor, no regulator. Is there anything wrong with this?
This will work only if you are able to maintain the junction temperature at 25C. Normally, this is not the case and the forward voltage of the LED will drop as it warms up. This will lead to a increase in the current, the current increase will accelerate the rise of the temperature and this "snow ball effect" may destroy your LEDs. Check page 7 of the document you added as reference, it is written that the thermal coefficient is around -2 to -4mV/degC. Another interesting aspect you have to watch is the range of the forward voltage, page 7 as well, it goes from 3.19V up to 3.99V. That means, you have to find one chip with exactly the 3.5V. If the chip you receive is in one of the extremes, you may have a overcurrent or no current at all according to your proposal.