In between infusions: Lid on or Lid off?

Depends on the room temperature, and the type of tea. In Japan there is a lidless kyusu called futanashi kyusu, used for teas that are brewed with boiling water, such as houjicha and genmaicha.

I have heard that green teas are often brewed lid off. makes sense since these are regarded to be sensitive to high heat

What about sheng pu erh or roasted oolongs such as dan cong?
brewing in a room temperature environment.

Another interesting question, after you are done boiling water from the kettle do you leave the lid open or closed. I usually leave it open because I worry about mold getting in there. But maybe I am silly.