Klyros, being "reptilian-like" in sense of skin at least, could also be reptilian in other ways? Seeing as there is a (somewhat strong) agreement on that Klyros isn't mammal, we can rule out both breasts and wider hips.
If they lay eggs or bear live young is more for settings team to decide upon really, but for both cases reptiles have concealed genitalia, so the clothing might just be a social thing to fit better with the other races.
My main point, the differences between the male/female Klyros, is that with most reptiles (and birds) the males have certain physical attributes to attract the female. If this were to be with Klyros as well, we're talking stronger colors, bigger wings/crests etc.
Last thing. I'm Klyros myself, so I didn't pick the reptilian angle for some "racist" joke thingy