Sorry to hijack, It is of some relevance to OP though and may offer a solution.
I had similar issue, slightly lumpy idle when the engine was up to temperature, fine when cold though, no misfire and initially no engine management light.
I changed temp sender first, checked for un metered air ingress ( post maf intake pipe, crankcase breather pipes either side of the throttle body, inlet manifold joints all ok and cleaned throttle body.
I then climbed the mountain and consulted Smaky
, he said oil in plug wells or pre cat lambdas.
The engine management light finally appeared I read the codes, P0130 and P0150 =
O2 sensor circuit bank 1 sensor 1 and O2 sensor circuit bank 2 sensor 1 (spot on again Alex)erased codes went for a drive, 20 miles ish the engine management light came back .
I changed Lambdas today, read and erased codes, no engine management light I went for a long drive no engine management light, idle is fine, engine feels a lot livlier too.
Oddly the lambda nearest the air con pump, bank 2 sensor 1( fed by cylinders 1 and 4 ) was very sooty, the bank 1 sensor 1 lambda however appeared to be fine just light grey deposits, yet the ecu threw up codes for both pre cat lambdas. (pic attached).The sensors have 72,000 miles on them so were probably both due to fail anyway
Was the lambda the cause of soot or is it a symptom of something else?
If the lambda had failed or was faulty would that cause it to become sooted up or is it the fact that it`s sooted up the reason it failed?
Anyhoo it idles as smooth as the preverbial babies behind now and goes like stink.