You do not need a PCR test for transit, only for entering Japan.
Here's the JAL page showing that:
Entry restrictions for each country quarantine Measures - JAL
Travelers who are not entering Japan and transferring directly to a third country by transit, are not required to submit any documents and undergo PCR tests.
here's the NH page showing it:
Information Regarding Travel from/to Japan and Other Countries | ANA Care Promise | ANA
Travelers who are not entering Japan and transferring directly to a third country by transit, are not required to submit any documents and undergo inspections in Japan. Nonetheless, travelers are still subject to the travel/entry restrictions and requirements of their final destination.
However, the following cases require entry into Japan. Please be informed that foreign nationals arriving from prohibited countries will not be allowed to enter Japan.
It doesn't matter if it's on one ticket or two, it has to do with whether you're entering Japan or not. And an international-international transit in the same airport doesn't require you to enter Japan.
That said, NH will inspect your required documentation at LAX for DXB. So, if you are required a PCR and/or visa, or whatever, to enter Dubai, they will deny you boarding if you are missing it. For my LAX-NRT-BKK trip, they verified I had my PCR and Thailand pass for entering Thailand. I was also dumped directly in to the international terminal upon arrival, no document check or any other inspection.