How exactly would one clean up piss on a lawn?  And why?

Anyone can sue anyone for anything, but why would it cost anything to pick up dog poop on a sidewalk or lawn?  I also seriously doubt that the occasional poop on a lawn would require re-sodding the lawn.  Heck...my own dog regularly poops on my lawn.  I pick it up and put it in the trash and that's that.  NBD.

That said, having your dog poop on someone else's lawn and not picking it up is a poopy thing to do.  Maybe contact your local police department to see if they'll be willing to issue a citation based on your video evidence.