Pictures will help. In my experience, brown tipped leaves come from incomplete hydration. Maybe you'll hear something else from container growers. But in my yard, those trees that are not established (i.e, roots haven't reached the upper reaches of the water table) I have brown tips. On trees that are established (i.e., roots permanently in the soil containing water) I have almost no brown tipped leaves. It is my understanding that lychees in their native range....southern China.....grow along river banks and have a constant source of moisture. So, watering is what I would look to first. If that isn't the issue, you have to go to plan "B" after some further head scratching.

Harry

when did you transplant the lychee? what are the growing conditions (temp, watering schedule, fertilizer, soil, wind protection)?

have you been having normal growths? are the new or old leaves browning?

brown tips can sometimes be normal in certain situation but need to rule out the usual causes

Too much water? You have to wait the new growth..and use a draining soil.