Hate to break it to you, toilets aren’t airtight. The particles go right out the side and tend to last longer in the air when the lid is down. It’s creates a reduction in visible particles as it seems the lid causes bigger particles to form so ergo less “visible particles” but they are just bigger and last longer for some reason versus the smaller ones. As has been demonstrated by the Mythbusters and many other studies, the biggest factor is having proper ventilation otherwise your gonna find shit particles everywhere regardless of if you close the lid or not.