Breathing the dust is indeed dangerous but when you consider the small amount you add to a sand filter, then how this is dispersed onto the lawn, my gut says there is nothing to worry about. You would have to be in a severe drought with the lawn surface totally dry for any dust to kick up. It will also quickly work its way into the soil and become harmless. If you had a DE filter you would be dumping a load of the stuff and then I would think before dumping onto a lawn. As for chlorine killing grass, I doubt it. The sun will break it down quickly and also consider that some municipal water supplies have somewhat high chlorine levels, not as high as a typical pool, and watering the lawn doesn't kill grass.
I suspect one of the problems with dumping quantities of DE into a body of water with fish would be the DE getting into the gills and doing harm. Probably illegal too. But then again, dilution is the key. What Carl said about killing bugs is true. The stuff is small and sharp and cuts bugs bodies.
Al