鲜 (fresh) is the operative word: lychee browns within a day of picking, so
鲜荔枝 specifically contrasts with
荔枝干 (dried) or canned. Du Mu's famous line
一骑红尘妃子笑,
无人知是荔枝来 refers to imperial couriers rushing fresh lychees to Yang Guifei in the Tang capital.