[SteverinoE93]

I recently bought a 2009 e93 with an N43 2 litre engine. 165k kms
Although the car looks perfect it has clearly not received the love and the maintenance that it should have.

It was delivered by the dealer with the engine management light on )long story - I was in Hong Kong and am moving to Spain).
It started with a P114C and 301 codes. I then replaced:
Coils, spark plugs, air filter, oil and oil filter.
Mechanic number one replaved the high pressure fuel pump and the thermostat (... not sure why)
Mechanic number two replaced the rocker cover (PCV) valve.
It was still idling very roughly.
I then took the intake manifold off as I suspected carbon build up on the intake valves. There was a lot of carbon built up - lovely job removing it.
It ran very smoothly for a few days but now has once again started to idle very roughly after 30 seconds. Engine management light comes on. If I let it warm up a bit, then restart it the engine management light goes off and it seems to run smoothly.
It runs fine when warm, but still idles roughly. Thi sis my 4th BMW and I never had any engine problems with the other ones.

I am suspecting the lambda sensors as they kick in after 30 seconds or so once the engine warms up.

Any ideas please as I am going mad with this and my wife is wondering if it will get fixed within my lifetime ....