I have a premium economy ticket with JAL and their website indicates I can use the Qantas lounge in LAX prior to my flight, is that correct?

For Qantas first, will need to have first class ticket or One World Emerald status to use this lounge.

The First Class lounge will not allow entry to anyone without a first class ticket. We flew Cathay Pacific First Class a few years ago, and we're allowed in some business class lounges will allow premium economy passengers but First Class won't even let in Business Class passengers. I am pretty sure you won't be allowed in on a premium economy ticket. You may want to check the business class lounge, perhaps. There's also a priority pass lounge (Star Alliance) that is really nice and may allow you paid access. Good luck!