F250 diesel running rough

Check your fuel pressure, early 2000 rams are notorious for fuel pump issues. They start but run rough or lack power.
Were the lean codes for both banks 1 and 2? (P0171 and P0174)

you may have to prime your diesel before it will draw fuel

I would chweck igniton first...miles? and previous service?

cylinder 8 is missing combustion which caused the o2 code the black box will not cause a specific cylinder to miss, there fore a fuel distribution problem is evident, the injector on eight is proablly the culprit the #8 cylinder is the last cylinder to be fed a fuel, pressure test is needed to determine if the fuel pump is strong enough to deliver diesel, ambulance spend a lot of time idling causing fatigued fuel pumps

Bad intake manifold gasket, head gasket, manifold pre-heat gasket, or any combination of them.

Gas or diesel having same problem, I'd start there to confirm fuel pressure . It may be pump running partially when cool, but when it heats up (the pump) it may be cutting out pressure wise. Not uncommon for a fuel pump to pump good when cold, then die once pump heats up from running. Still makes noise, but isn't supplying any or enough pressure.

If it is cold where you live and this a cold start situation it could be a glow plug or glow plug relay problem.

P0301 = Misfire cylinder #1P0303 = Misfire cylinder #2
P0171 = System too lean cylinder #1
Are you sure on the P1151 code? I am thinking this may be a P0151 which is O2 sensor related.
This looks like you have a fuel system related misfire. I would do a fuel injection cleaning service and then clear codes and see if the codes regenerate.

CK FUEL FILTER, AS WELL AS AIR FILTER , THEN HAVE SOMEONE TO CHECK GLOW PLUGS AND GLOW PLUG RELAY

It sounds like a problem with your computer or injection system. the computer controls the amount of fuel put in the cylinders when you step on the gas. But it sounds like your truck's computer is having problems controlling this and when you accelerate hard or are towing and step on the gas, the computer just pumps diesel into the cylinders which causes the rough running(i assume misfiring and what not) and the loss of power. But when your not towing or accelerating hard, you are better controlling the amount of fuel going into the cylinders so there arent any problems. Go back to the dealer and tell them there is a problem with the injection system and it adds too much fuel when you try to get a lot of power out of it.