Could be a lot of things. A few things that come to mind in no particular order:
Glow plug wiring. (The plugs may be new but if they get no juice.....)
Bad injector spray pattern. (Thick droplets cause a rough idle when cold but run great when the engine is hot.)
Stretched timing chain. (It will ****** pump timing. (Mine was junk at around 130K)
Low compression it 1 or more cylinders. (Low compression makes a diesel idle like hell when cold. After they warm up it will run smoother)
Non OEM glow plug timing box. I replaced the one on my truck with a NAPA unit and it flat out sucks. I have to glow it twice in the mornings because the thing is junk. It won't glow the plugs long enough on one cycle to start the engine on a very cold morning let alone give it a nice idle.
The lift pump will have nothing to do with your problem IMHO, but here is a way to check it. Start the truck up when cold and immediately turn it off. You should hear a thump, thump, thump, under the drivers door for at least 5 to 10 seconds. If you don't, 99.9% of the time it will be the junk oil pressure trigger switch they put on these trucks.
Good luck and have fun.
🙂
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