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Actually, lime dust is not good for dogs to breathe in or for their coats and pads to rub on.
Believe it or not, eliminating odor from a outdoor kennel run area or back yard is pretty easy with products designed to digest urine and stool and turn it into odorless gasses.
One of the most popular is Odor Mute C, which you can use in a hose end applicator and as it comes as a powder you can mix it as strong as you like. You can get it at http://www.upco.com/. If you decide to look for a product on your own or would like to use another cleaner, just look for one that has enzymes to 'digest' the odors. These are safe for the dog and plant life and work on cement or dirt or grass or gravel etc.
You may have to apply a couple of times at first to eliminate built up odors but then you can work at using it on a schedule to keep the run area clean.
You can also try plain old bleach and water. Just mix. 1 part bleach to 25 parts water. This strength can deodorize an area but please remember not to put your dogs back in the yard until the bleach has dissolved into the ground.
I hope this helps!!