The rust like appearance on the leaves of the lychee tree is a very common occurrence. It is not a disease but rather is caused by a tiny mite (Erinose mite) about 1/200 of an inch long. The foliage has been described as curled, distorted and galled, with a velvety brown to brownish-red appearance on the underside. These mites attack new leaves at the onset of growth flushes.
Mites infesting young trees may cause a stunting of the tree. At this stage, when trees are manageable, infested leaves can be removed and discarded. This will help reduce the mite population and allow the young trees to grow more vigorously. Generally as a tree becomes larger, removing infested leaves is difficult. However, mites seldom kill a tree. It’s probable that the tree will continue to be plagued with mites, but you should be able to harvest a normal crop of fruit.