Update! Don't oil it, at least not the under side. I cooked some fried rice in my wok. We ate some, and i covered the wok and rice with my lid. After about 30 min, i took some more rice, it smelled and tasted strange. I think the lid collected moist and some of this moist dropped back to the food, i couldn't eat it. I washed the lid few timed in the dishwasher, lid is fine, and i think (i hope) the problem is solved. That's how you learn 😊