Q.My Asiatic Lily Has 3 Buds On It. The Older One Hasn’t Bloomed Yet . But A Younger Bud Has Started To Open Its Petals.
I bought it from a nursery 6 days ago. The plant is placed in partial shady location.

Certified GKH Gardening Expert
This plant was, likely, forced to bloom. They will not normally bloom at this time of year. With that being said, the failure to bloom properly is more than likely due to many environmental factors at this time.
They will also bloom better the more sun that they receive. If it does not bloom by summer time, then you may need to put it in a sunnier spot, or add horticultural lighting.
Here is an article that will help with their care: https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-lilies-in-containers.htm