I keep my lid closed. The thought is that there will be less air flow to keep the pellets burning longer. That may or may not be true, but it is my story and I’m sticking to it.
I think with it closed, it provides better air distribution throughout the barrel. Otherwise, the air just leaves out through the opening. Plus, as mentioned above, it helps to dry out the grate/crud.
Closed. The only reason I can see to leave it open is to speed up cooling, and several to leave it closed, all having to do with precipitation. I opt to leave it closed.