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These are pretty sensitive to any air leaks. Make sure that your oil cap and dipstick are both seated fully. With the engine running, try taking the oil cap off- see if it sucks down really hard and is difficult to remove.
Otherwise, I would suspect the Mass Air Flow sensor...
What are you using to scan the fault codes?
You may want to try spraying the MAF out with some electrical cleaner (something that will not leave any residue) and see if it returns.
These systems are pretty smart- if there is an O2 sensor not reading correctly, it will detect it. I think that even if there was bleedthrough from the two systems, the engine management is designed to take that into account (as it has to work at the time that fuels are switched, which would result in some blending)
An O2 sensor ONLY detects oxygen- not any other gas- so if it is saying you are running lean, then it is reading too much oxygen- which can also happen if you are getting an incomplete burn in the chamber, like from worn spark plugs. It can even happen because of a leak in the EXHAUST system, in front of the O2 sensor.
If the oil cap area is sucking too hard, that would indicate that the crankcase vent it open to the intake. It pulls lightly at idle, maybe hold a sheet of paper in place but not enough to hold the cap down.
I've seen a lot of issues with the PCV systems causing these kind of problems, or running rough at idle.