Engine shakes after warm up - 2001 Lexus IS 300

perhaps some water condensation in the empty tank that then caused the smoke and shaking during warming up.

Refill with good branded Diesel a full tank and have a drive for 30 mins possibly warming at high revs (or low gear to warm faster)
Enjoy

first check for vacuum leaks, rubber vacuum lines can dry out and crack especially after sitting for a while

May have jumped timing. Check that first.

That means there is a leak in the block engine to the combustion chambers one of the cylinders is bad.

it could be the ignition coils spark plugs or the timing, would have these checked.

could ge a leaking injector flooding the engine at start up, or coolant getting into the combustion chamber, either intake or head gasket, do a pressure leakdown test on both fuel and coolant,

sounds like you may be experiencing a misfire has tune up been done lately if not do one if you find a cylinder not firing you will need to determine if the misfire is due to spark arcing to ground ie bad plug wires,cracked insulator on plugs crossfire etc. or is it caused by fuel keep in mind in my shop we replace alot of nissan and acura fuel injectors which can cause this also when you first start car computer richens up fuel system then leans out as car warms up you could have vacuum leak that is compensated for when first started once warm and lean the vacuum leak causes a to lean condition that results in your shaking hope this helps and does,t confuse you good luck and repost if it does not help

check engine coolant temperature when it gets warmer, or at operating temperature, and verify that the temperature gauge is showing warmed up to operating temperature. If the coolant temperature sensor tells the computer the engine is cold it will over fuel and miss and the engine will die. When cooled down it will run fine until it warms up. Also could be coil if it starts missing after warmed up.

the p 0300 codes gives you the clue
it is random misfires and that is predominately from injector and low fuel pressure
pulling a plug lead will amke no difference if there is no fuel in that cylinder to ignite
bad coils will be a constant miss regardless
try putting a can of quality injector cleaner in the tank to see if that fixes the problem
have a fuel pressure tset done to check for pump, filter or pressure regulator problems

Is it idling too fast? More the 850 rpm?