The Collaborative International Dictionary of English v.0.48:

lichee \lichee\ n.
   1. A Chinese tree (Litchi chinensis) cultivated especially
      in the Philippines and India for its edible fruit, the
      litchi nut; sometimes placed in the genus Nephelium.

   Syn: litchi, litchi tree, Litchi chinensis, Nephelium
        litchi.
        [WordNet 1.5]

   2. A Chinese fruit having a thin brittle shell enclosing a
      sweet jellylike pulp and a single seed; often dried.

   Syn: litchi, litchi nut, litchee, lichi, leechee, lychee.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

litchi nut
    n 1: Chinese fruit having a thin brittle shell enclosing a sweet
         jellylike pulp and a single seed; often dried [syn:
         litchi, litchi nut, litchee, lichi, leechee,
         lichee, lychee]