The short comment I posted should be classified as a quip.
What it actually insinuated is there is a very short list of operating and maintenance procedures for toilets. If you are to the point of closing the lid to contain odors, some of those basic steps might be getting missed. Hence, the quip.
Actually it doesn't, flushing with the lid closed can leave the particles in the air for up to around 11minutes longer as they exit the side of the toilet with more velocity and pressure. It's not a sealed system.
Yeah, I'm aware that toilet lids are not an airtight system, I've seen them. It still does slow down airflow enough for most of the poop to settle instead of spreading to your whole house.
No it actually does not, it increases the spread and creates a pressure build up compared to being open, you are initially adding volume into the toilet when you flush with the lid closed this pressure build up is greater and spreada the particles further. You are essentially creating a shit nozzle on the sides of your toilet. All the lid does is help the particles become bigger so there are fewer visible particles but they are bigger and travel further, while remaining airborne longer due to their velocity.