Is it bad to give my dog a bath on our lawn? Will the soap residue end up killing our grass? I never had a second thought about this but I've recently come across some natural weed killer suggestions that use soap as an herbicide.
It's all about ratios - the ratio of soap to water, and the type of soap. I shouldn't imagine you're using anything too noxious to wash your dog, and I assume you will be rinsing him off in the same area, which will dilute any soapy solution on the lawn. Just use the hose or something to wash the lawn off a bit more after you're done - so long as you're not doing it very frequently, it should be okay.
Too much water will drown the lawn and squeeze the life out of it. I put a Slip N' Slide out on my back lawn for a party and, of course, the lawn turned brown under where it had been all day, but also it browned where just the runoff was nearby. I decided it was because the kids were running all over that area and "squeezed the life" out of the grass. That said, I just drove my pickup up the inclined part of my lawn with about 800 lbs of dirt and stone in it. Tomorrow it will be fully loaded with soil, weighing at least 1500 lbs; and Thursday comes the mulch. But I am careful to never drive on the lawn when it is wet. I also use 4 wheel drive to clime the incline so the wheels don't spin.