The tree gets hardier as it grows older, but needs protection from the wind. The brown tips seem like standard equipment but the more balanced citrus fertilizer should help. Lychee seems to like damp conditions with an even supply of water through the year. Mulch the tree to help water retention, but keep mulch 1-2 inches away from the trunk. Water the tree about twice a week if there is no rain.
Lychees seem to like the inland muck soils better than the sandy soils along the coast.
You are looking for the Indian tamarind , which lasts in strong hurricane winds. It produces edible pods used in chutney and is a good, long-loved shade tree. They like full sun, a somewhat moist location, and abundant fertilizer. Bananas also like a good permanent mulch around the base of the clump. Recycling old banana leaves and using them for the mulch is a good idea as the leaves are high in phosphorous.