As a record rotates, the air closest to the surface gets accelerated towards the periphery, drawing a steady stream of air down around the spindle. So reduction of air-born dust suggests closing the dust cover during play.
A dust cover also acts a bit like closing a window, and it will attenuate external airborne vibrations from reaching the cartridge. My Garrard 301 table is in the same room as my speakers, which are either dipole Quad electrostatics or KEF Reference 1 with rear ports. The dustcover is an acrylic affair made by SME and is voluminous with plenty of space. I am very surprised that the sonic effect of closing my dustcover seems to be subtle to non-existent, at least to my ears.
Obviously, there is acoustic output from the needle / cantilever which is partly airborne and partly transmitted through the vinyl record, I am using a 5-mm Achromat to absorb record reflections and transmission to the platter, which leaves those airborne sounds we can just hear if we are close enough. They will reflect internally from a lowered dustcover but I would have thought the sound level would be far less than the speakers generate with the lid open!
So I put the lid down unless i forget!