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:

• A. Observant of customs or rules, especially social rules; civilized.
• A-2. Observant of duty to gods and men; righteous.
• B. Equal, even, well-balanced, fair, impartial; legally exact, precise; lawful, just, right; fitting.
• C. I don't really understand the glosses here; they seem to refer to justification or lawfulness: bound to; have a right to.

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”.