KRDR, just water the spots where the dog pees well -- diluting the urine and washing it through, and the grass will be fine. You don't need any product other than a garden hose connected to a water spigot IMHO.
Train your dog to potty in a specific area. We are fortunate to have woods surrounding three sides of our yard. We've trained our dogs to go "in the woods". If you don't have a treed border, just pick a place in your yard and bring your dog there every time they're out for a potty break. It may take a couple weeks, but if you are consistent and give them a specific command they should catch on. And this way, you only have one area to keep clean. Good luck.
Yes, it's terrible, huge brown spots. I can't always find where they have gone soon enough to hose it down. I would like to teach my male to mark on plants rather than going on the lawn. How do you teach them to lift their legs to pee?