I verified today in MEL that "Partner Platinum" via Diamond on Delta will NOT give you eligibility to upgrade to business on the LAX route.
Surprisingly (to me anyway), I also could NOT upgrade to premium economy either, despite the availability.
For additional data: there was 1 business left and an undisclosed number of PE. The upgrade price point was A$2500 for business and A$999 for PE. I would be curious to know if these are static upgrade prices or if they are dynamic based on inventory remaining and possibly day of the week of travel.