Location:
To grow a healthy lychee tree, start by planting it in a good location. Lychee trees need full sun so you should plant them away from other large trees and you should plant the trees at least 10 feet away from buildings. Shaded areas of the lychee canopy will generally not produce fruit so if you are planting the tree for it's future fruit production you should pay attention to your tree's level of sun exposure.
The new growth of lychee tree(s) is very delicate and easily damaged by the wind. Wind damage can severely impair the development of a small lychee tree and destroy new growth before it has a chance to develop and mature. Plant your tree in an area that receives some measure of wind protection.
Soil:
Lychee trees originated in the rainforests of southern China, where it is not unusual for trees to reach heights up to 100'. For best results, you should attempt to simulate the soil environment of the natural lychee habitat, which is rich in organic matter, moist with good drainage and free of artificial components like perlite or vermiculite.
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A lychee tree will provide some natural organic matter to its soil zone through leaf and occasional branch litter and any fruit drop that occurs. However, you need to supplement the area above the root zone (slightly out past the drip line of the tree) with mulch and organic composts.