We use a dog lot for a run also, and have never had any problems with predators. We also close them in their house at night. Its going to get muddy, the best you can do. Ours is on a slight hill for drainage, and I learned that by elevating the low corner up on a brick; alot of the mud is washed away. Before I started elevating it, the chickens scratch(alot),and it would build up in the low corner, kind of bowl out the center, and make a mess. Nobody on here is going to tell you thats safe, and I only do it because my chicken run is in a safe location, away from any predators.I tried covering it, but eventually the mess builds up. the hillside drainage, elevated corner,and full sun has all but taken care of my problems, at least a day after the rains are over. If you can rotate it, you will be better off. Here are a couple of pics, I have two runs connected to my coops for an area of 600 sqft. The first pick shows the upper corner joining the coops, the second shows the low corner. You can see there is no grass even in this large of a run. The chickens are out for their weekly grazing.