I was curious

Recently, Best et al13 flushed a toilet seeded with fecal suspensions of Clostridium difficile. Settle plates were placed near the toilet and air was sampled at seat height, flush handle height, and midway in-between, with the toilet lid both up and down. Settle plates showed widespread dissemination of large droplets with the lid up but not with the lid down. C difficile was recovered from air sampled at heights up to 25 cm above the toilet seat and up to 90 minutes after flushing, at concentrations 12-fold greater with the lid up than with the lid down. They concluded that lidless conventional toilets increase the risk of C difficile environmental contamination and thus discouraged their use.

https://pmc.ncbi.nlm.nih.gov/articles/PMC4692156/