Actually, the lungs/coughing issue is explained in the Clone Wars animated series they had on Cartoon Network. The second season of Clone Wars takes place right before the opening of Revenge of the Sith--as in, one of the main plots of the cartoon is "Grievous lays siege to Coruscant and captures Palpatine and takes him to his ship, setting up the first act of RotS."

And right as Grievous is taking off with Palpatine, Mace Windu crushes his chest, and he doubles over with a giant wheezing coughing fit. What I wanna know is where'd he come from and why does he have biological bits, but that's probably explained in one of the novels or something.