I suspect that to a certain extent you can tell by the shade of pink or blue, just as you can with mined diamonds. You can see in my blue, for example, that it's not irradiated, just because it's such a clear blue. You never get that colour with irradiated diamonds.
I'm sure Eric will have an answer.
Colored lab diamonds get their color in the same way that natural colored diamonds do. Actually, in most cases, treated diamonds are getting it the same way. Natural radiation can be very similar in effect to radiation treatment done in a lab and the impurities that bring on the color in synthetics are naturally occuring as well. The result is that the only definitive way to tell is with some very techy tools and sometimes even that is tricky. As a consumer that’s out of the question and, realistically, the way you tell for sure is by looking at the lab report. The best clues are often from the color itself and, in a backhanded way, from the price since certain natural stones are VERY expensive and certain treated stones are remarkably cheap. If we’re talking about buying a stone it’s easy enough. DO NOT buy a natural fancy diamond without lab work from a credible lab no matter what the seller claims is the origin of color. Separating treated stones from synthetic stones is usually a little easier but it involves a microscope and knowing what your doing. Sometimes it’s pretty easy but this too can get beyond the sort of thing you want to do as a consumer. Do it with the paperwork.