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. Use a citrus fertilizer on bananas in March, June, and October. Water plants when it is dry. Bananas can form within 20-24 months after emergence of shoots from the ground. This happens only if they are well fed.