How to calculate the energy output (in Joules) from an LED
Your question is about efficiency of a LED emitter. You can't calculate the efficiency, it is a design/manufacturing parameter. Some manufacturers do specify the light output in terms of power, so it should be possible to find the answer to your conditions in easy way. The parameter varies wildly, with LED bin, and chip temperature. For example, this LiteON LTPL-C034UVH405 UV emitter has more than 50% efficiency, at 3.9V and 700 mA (2.73 W of input), it emits 1.375 W
of light with spectral peak of 405 nm, according to the datasheet.