The cause of your leaf spots is most likely anthracnose, a fungal disease that causes black spots, often with a yellow halo, and can result in mild to severe defoliation. Black walnuts are particularly susceptible to anthracnose. The good news is that it rarely kills an otherwise healthy tree.

You should remove affected leaves and prune out infected twigs if possible. Rake and destroy fallen leaves and nuts. Wet conditions promote disease so avoid or redirect sprinklers that wet the lower canopy of the tree. These practices are to reduce the potential of the fungus overwintering and reinfecting the tree next year. Keep the tree healthy through regular deep watering.

You can read more about the disease here: http://pnwhandbooks.org/plantdisease/walnut-juglans-spp-anthracnose