An Emerald member departing on a OW flight in any cabin will get access regardless - connecting or orginating in Sydney
For a non Emerald member : With a connection from a 1st class OW flight to a shorthaul OW flight ( 5 hours or shorter ) in any cabin will be entitled to access the 1st class lounge

With separate tickets, I believe that Qantas still gives access as if it was a through ticket