If SYD-LAX and LAX-NYC are different flight numbers, ii will count as two segments. If it's the same flight number, if you're stay at LAX is under 24 hours, you have a direct flight, so one segment for the entire SYD-NYC direction. However, if you stay more than 24 hours at LAX, it's a stopover and you get two segments, even if the flights share the same flight number.

BTW, despite Bourdain's series, layover has no clear meaning, so it's better always to say either stopover or connection (but note that if you have separate tickets, you don't have a connection).