Does the inside of a lid used to cook rice or steam vegetables have anything besides water on it?
Starchy foods, like rice, tend to bubble and splash.  They will get starch on the inside of the lid.  If you don't let it dry out, you might decide a quick rinse is sufficient, but if it dries it will probably need a proper wash to remove the starch.
Steaming is more interesting.  There shouldn't be any splashing above the level of the food, so it should just be clean water on there.  I'd rinse it before drying and putting away.
That's a minimum; I would just put mine in the dishwasher; there's often a space when it's otherwise full that wouldn't be much use for something really dirty.