Trying to relate the issue of lazy relativism or moral facts to "the dress" is, excuse me, scientifically underinformed.

"The dress" genuinely appeared different ways to different people, because their visual systems were primed to interpret the lighting in two different ways. Prior expectation primes perception! This is a fact, one that each and every scientist of vision asked about "the dress" mentioned, very clearly and explicitly.

So in fact, "lazy relativism" about "the dress" is correct. It really does look white-and-gold to some people but blue-and-black to others, because of how our visual nervous system primes itself. And, last I heard, when you get a photo of the damned thing in normal, non-washed-out light, it looks blue-and-black, so we get a correct answer at last.

The distinction between "the dress" and moral facts is that few moral philosophers can agree on either a single test that can, given the time, be performed to establish a moral fact, analogous to photographing the dress in a more normal light where everyone's visual systems will see it the same way. We could try to treat the difference of moral opinions as a social- and moral-psychological issue, and look for a psychological/cognitive mechanism underlying our failure to come to some shared moral discourse, but unfortunately many moral philosophers categorically reject the notion that moral psychology has anything to say about morality as such.

So in fact, "the dress" is both amenable to relativism and to finding a final correct answer in a way that morality usually appears not to be.

(Of course, in my view, it usually appears unresolvable simply because most moral philosophy tends to be founded on a combination of ungrounded intuitions and extremely shaky metaphysical assertions, which then result in irresolvable discursive problems. There is such a thing as real morality, but almost everyone seems to prefer to ignore it while discussing moral philosophy, despite its being more-or-less the first thing we resort to when confronted with actual decisions to make in our own lives.)