Andy is spot on, lid down will reflect the heat back and melt any cheese. It will also help cook anything through faster, like if you put a frozen burger patty on to cook... like I did for lunch today.
It really depends on lots of variables, like what you are cooking; what is your initial temp, are you only cooking one food, do you need to plan for something being finished on the stove...???
I never have a fixed lid up or down for anything, unless I am finishing off some melted cheese or keeping grilled items warm :^)
Give us this day our daily bacon.