This actually sounds like a fun math problem.
There's more than just the angle off from the horizon to consider though, since strictly speaking the sun would only achieve zenith once a year (twice if the location is on the equator). Lumberyard's sky doesn't match anything equatorial, and likely is trying to evoke something like the Pacific northwest. Seattle, for example, is 47 degrees N latitude. A handy solar calculator here gives the elevation and zenith angles:
http://www.esrl.noaa.gov/gmd/grad/solcalc/. I forget how Source defines its coordinate system, but I think the 65 degrees mentioned before is the elevation angle, not the zenith angle. (zenith angle = 90-elevation angle).
To do this properly, we'd have to decide on the time of year of the skybox, and an approximate latitude of the location. Once those are chosen, we can find the approximate time of day for a 65 degree solar elevation.
Yes, I way over thought this. It beats grading final exams.