John:
I'm a dog owner but these kind of stories really annoy me! Not having a go at you, but at whoever the owns the dog sh*tting on your lawn.
There's no obvious solution but to either find out who owns the mutt yourself, or contact your local dog warden and try to get them to do it.
If by chance you see the mutt on your property, perhaps you could if poss get a hold of it, labs are known to be docile, put it in your garage or wherever and contact the dog warden to come and collect it as a stray? That way, you wouldn't have to come into direct contact with its owner and the pr*t may just get the message, if you follow me?