I don't know any Greek, either modern or ancient, so I can't judge the LSJ entry for myself. Here's a summary of the English glosses:
This is woefully insufficient for me to understand the matter on my own. Just from this, it's not clear to me that the word means moral and not simply right or just, or perhaps what we might call "proper behavior". These things are certainly related to morality, but they also seem consistent with descriptions like “excellence of character,” not “moral virtue”.
I was stunned to read the accounts quoted below. They're claiming that the notion of morality - in the sense of there being a special category of things that you should or should not do for the sake of the things themselves being inherently right or wrong - might not only be a recent invention, but also an incoherent one. Even when I had read debates about e.g. moral realism, I had always understood even the moral irrealists as acknowledging that there are genuine moral attitudes that are fundamentally ingrained in people. But I hadn't ran into a position claiming that it was actually possible for whole cultures to simply not have a concept of morality in the first place.
I'm amazed that I haven't heard these claims discussed more. If they're accurate, then they seem to me to provide a strong argument for both deontology and consequentialism - at least as they're usually understood here - to be not even wrong. Just rationalizations of concepts that got their origin from Judeo-Christian laws and which people held onto because they didn't know of any other way of thinking.