When peace lily leaves have problems the first thought is we have a watering issue. However, it sounds as if you have that under control. Was the peace lily exposed to a great temperature fluctuation? Sometimes temperature changes can cause problems in peace lilies and they stress when they have to acclimate to new situations. Are you getting any new growth and is it turning black as well? If this is the case you might have a Phytophthora fungus issue with your plant. Removing any infected leave is the best course of action although you can use a fungicide to take care of the fungal problem.

Although peace lilies are fairly resilient, they tend to take a while to recover from any stress. So, if you remove all the damaged leaves and the spreading stops be patience and give the peace lily time to recover. The key is to look for new growth and watch it.