outside the law of Moses: not living under Israel's law, and so a Gentile
Greek built this word by putting "not" in front of "law," and in this first sense the negative is simply factual. It describes people who were never given Israel's law and so do not order their lives by it. That is a statement about where someone stands, not a verdict on how they behave, and used this way the word comes close to a plain label for a Gentile.
Paul is the only writer who uses it so, and he uses it with care. Describing how he adapts himself to reach different people, he says he became like one outside the law in order to win those outside the law, and then guards the point at once: he is not free of God's law but bound within Christ's. The same word does double duty in a single sentence, first as a neutral description of the people he is trying to reach, then, in the phrase he denies, as the moral charge he wants no part of.
That guard is the clue to the whole word. Not having the law of Moses is a circumstance a person is simply born into. Standing outside God's claim altogether is something else, and it is what the word's other meaning names.