I am flying EK J from NCL to DXB, and then connecting to a QF Y flight to SYD.

I am flying EK J from NCL to DXB, and then connecting to a QF Y flight to SYD. Will I be allowed access to the EK J lounge in DXB?

I don't think you will be allowed access to the J Lounge in DXB unless you have a Qantas Club membership and this would only be if your SYD flight is ticketed with a QF flight number.

That's correct. No "arrivals" access at DXB otherwise.

According to the Qantas website, the answer is no in Dubai - your onward flight must be in business class to gain access, or you'll need to be a Qantas Club member or an elite frequent flyer.