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Unless you live in a warm climate, it is best to grow peace lily indoors or in a container outdoors for easy overwintering inside. They cannot tolerate cold at all. In addition, outdoors they require bright light but not sunlight, as this will quickly scorch the plant, which may be what has happened with yours. You can cut away the spent bloom and make sure it is located in a suitable area. Partial shade is best. Also, ensure that the soil is kept evenly moist but not soggy.

If you live in a generally warm climate, then yes, your peace lily can be grown in outdoor shade. If you're unsure, allow it to grow in a container placed in the shade where you can bring it back indoors whenever needed.

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This article will help you with treating root rot: https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm

These plants do well in indirect light (no direct sunlight) and will even thrive in low-light areas. Peace lilies prefer an evenly moist soil. The soil never should be soggy and the plant shouldn't sit in water. Allow the soil to dry between waterings. Fertilizing is another important factor in caring for these plants. Feed the plant once a month during the growing season with a standard houseplant fertilizer, such as 20-20-20, at half the recommended strength. Repot the plant every year or two with an equal mix of potting soil, peat moss and sand. Regularly wipe down the foliage with a damp sponge to remove dust or place the plant in the shower to keep the foliage clean.