The brown water may not be anything to be concerned about. The water that drains through the container can be the result of the organic components in the soil mix. However the droopiness of the plant could be a problem. Drooping can be a sign of under- or over-watering. If it's underwatered, the plant will revive after getting watered. Peace lilies do not like to be kept constantly wet. Over-watering can result in the roots rotting followed by wilting of the plant. If the container is sitting in a pan or saucer that collects the water that drains out, and that water isn't poured off after an hour, the soil remains too saturated. The soil should be allowed to dry to the touch before you water again.
