The verb [当]{a}[た]{ta}[る]{ru} has many "meanings" translated to English, but there is a core sense in them of being on target, hitting a bullseye, being exactly right. It's an intransitive verb in all of these cases, even though we would need transitive English verbs to translate them - it is vital to keep in mind that languages are not just arbitrary collections of labels for an agreed-upon set of concepts; they reflect the thought processes of their originators and the evolution of those world views, in a cultural context, over centuries if not millennia.
My guess about the underlying idea is that the "target" isn't seen as a direct object in Japanese because the action of 当たる isn't about the striking, but the precision. Winning a competition, or a one-on-one contest, would normally use a different verb [勝]{ka}[つ]{tsu} (although this is also intransitive!); but 当たる makes sense for a lottery, I think, because the point of a lottery is that you're trying to guess numbers and get them exactly right. (English can make a distinction as well; it would be strange to say that you "defeated" or "were victorious over" a lottery.)
Perhaps "be accurate" works as a gloss for the central meaning. That's intransitive in English, too.