1994 BMW 540 BMW 1994 540i, rough idle, no acceleration, 12

So the 540i has 150,000 miles on it. Has a rebuilt transmission (at 110,000), rebuilt engine at 65,000 for some recall on the M60's (previous owner), new cooling system.

So the problem is one day I turned it on and the engine was super rough and check engine light was on. Checked the codes and it gave me a
1222 Lambda Control 1, here what it says about it:


T"his code is stored when the DME detects excessive
deviations in the air-fuel mixture (too rich or too lean) for longer
than 10 seconds. Possible causes: Fuel tank ran empty,
Incorrect Fuel Pressure, Injector valve defective or coked,
Engine Temperature Sensor defective, Secondary air leak,
Fuel evaporation control system defective, Air Flow Meter
defective and/or the combustion is being disturbed by
mechanical failure (Spark plugs, compression,
intake/exhaust valves ect"

Problem went away after driving down the road about a mile, took it into the shop and they told me it was going to be $1300 fix and they had to replace my motor mounts because they were colapsed (smelled BS). Mabe so but I don't think the motor mounts have anything to do with my problem. Had them replace the spark plugs and thats it. Problem started again and will go away periodically.

SYMPTOMS: rough idle (gets better after you drive it for the day), pressing gas pedal in the morning yeilds little no acceleration until after you drive it for 15 min then it gets better, when I release the gas pedal and its not accelerating and I lift off it the car will "jump, " engine shakes pretty bad. You can see it move about half inch when its having the problem, exhaust pipe- you can feel the exhaust pop randomly with the engine shake, feels like a couple of the pistons are not firing when you idle, (then again I don't know what that would feel like)

Here is what the mechanic said:

"the codes we got could be set if 1 oil has not been changed enough and has fuel in it 2 you ran out of gas 3 the oxygen sensor on bank 2 is bad. Mechanic tested for any vacuum leaks that could effect mixture and found none. It is still possible to have a vacuum leak at the maniold when the engine is cold and first started. Check of spark plugs show they are worn and there is oil leaking from the valve covers. Replaced spark plugs."

If you help me it would be great.

One more thing. When I park after driving it you can smell something that sort of smells like burnt plastic.