Lambda Sensor With Oil/leakage Oil?

Hello and welcome to the forum, Escala.

 

Extremely unlikely to have oil escaping from O2 sensor. Suspect there is either an oil leak or oil sweat from somewhere above the sensor / exhaust. Clean area with engine or brake cleaner, take some silver / kitchen foil & place above senor / exhaust, this will collect oil from offending area with engine running. Hopefully this will help you to get to the bottom of the culprit. Let us know how you get on.

 

Not entirely sure if I get what your trying to say.
But I'm guessing you have an oil leak, which is hitting the exhaust near the sensor. This is then giving the impression that the sensor is smoking. There is nothing that could make the sensor smoke (except the oil)
First thing I would try is, if you think the filter is leaking is try giving it a little tighten, or change it.

 

Hello I’ve just changed the oil on my speed triple and when I unscrewed the oil filter some oil got onto the exhaust in that area near the lambda sensor. It smelt a bit of oily smoke when I started it despite me cleaning it as well as I could. If your bike has recently had an oil change it could be that the oil filter has not seated properly or hasn’t been tightened to the correct torque, I believe it’s only 10nm, so not a lot.
Give the area a good clean with some degreaser and check for leaks with the engine running.

 

Is it definitely oil?
Hard to diagnose over the internet but....
One of the results of burning hydrocarbons (petrol) is water. Water mixed in with carbon creates a black liquid; could this be what you are seeing?

 

Basically there are two places the oil can leak from, one is the sump drain plug and the other is the oil filter, both easily seen if you get down and look under the engine. That’s the good news. The bad news is oil can also leak from a cracked sump or a leaking sump gasket and you really don’t want that as it’s not a straight forward fix. Give the area a good clean and start the engine noting where the oil is coming from and repair accordingly.