Just allow me to stick my neck out for a bit......
Some diesel engines require high lubricating oil pressure to build before the injectors will open......this is why a cold start isn't absolutely instant, it takes a second or two of cranking before the thing will go. This used to be a huge issue with the Izuzu common rail engine as found in the Trooper.
The diesel fuel however is pressurised to a huge degree, and fed into the 'common rail' (pipe, for want of a better explanation) where each injector receives its fuel supply.
So - we are talking about two different things here 1)The lubricating oil pressure generated by the engine, which is determined by the condition of the engine, together with the oil quality and filter 2) The performance of the high pressure fuel pump, driven by the timing belt, often enough.
I think you need to find a diesel specialist who can measure the pressure of both pumps, but my guess would be the diesel pump which unfortunately ain't cheap
The high pressure pump always puts the EML on when it is faulty, if the lube oil pressure is down, then it often doesn't.
John