Q.1 month after blooming my Lily leaves started turning black and stems getting soft what do I do?
It’s a tiny skyline Asiatic lily.

Certified GKH Gardening Expert
This is showing a very classic symptom of overwatering, leading to fungal infection. Most of the time, this will not lead to the death of the plant but will affect it until dormancy. You can help them along by adding just a 1/4 cup of DOLOMITIC LIME and a full tablespoon of WETTABLE SULFUR to the soil around it. This will help kill off the infection and condition the soil.
I would also hold off on watering until the top 2 or 3 inches of soil is COMPLETELY DRY. You can check with the tip of your finger. This will prevent overwatering in the future, but the rain should be more than enough to keep it healthy. If you get large amounts of rainfall each year, then you may want to apply the treatment mentioned twice per year.
This article will help you with their care: https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-asiatic-lilies.htm