This seems like something that should be true, but I think I remember seeing a Mythbusters episode where they decided it didn't make a difference. That show was more about entertainment than science, so I wondered if there was a more rigorous study done? I've definitely seen splashes of water(?) come out from flushes so that alone seems to argue for closing lids.
I seem to recall that Mythbusters episode proving the exact opposite. They showed that fecal matter definitely gets sprayed all over the bathroom when the lid is up when flushed.