yes, Lilies do like full sun, 6-8 hours of light a day. This one does appear to be at the end of its blooming cycle. The flower petals will turn brown and fall off. You are then left with the plant and the flower stalk. You can cut off this flower stalk, unless you want it to make seeds, then leave the flower stalk. At the end of the growing season, which I am uncertain when that is in the Caribbean. I would think it is the winter there now.
Here is the thing. You have a plant that has been grown in an artificial environment, given the right amount of light and warmth to force it to bloom. They sell these forced lilies even during the winter months. They go from perfect growing environment to something they are foreign to. They then most often start to shut down really soon. Then they go dormant. It is often very difficult to get these forced lilies to survive for long periods of time or get them to rebloom, because of the way they have been grown up to this point. I just wanted you to know that.
I am not sure if lilies grow in the Caribbean. They need a cold period in order to survive. Which means they need to go to sleep in winter. While under ground be exposed to cold temperatures for a period of time before they can grow again. I am not sure you get that cold period there. After you plant goes dormant, you may have to lift the bulb and store it in a cold place for a time being.
Enjoy the flowers while you have them. Enjoy the green plant as long as it stays actively growing. After that point you will have to decide what to do. Throw it away or store the bulb in a dark dry location for many months.
Good Luck and Happy Gardening