Ah, I see. Have you tried exporting as .obj and reimporting that .obj into anim8or to make sure it's exporting everything correctly? Also, some programs separate the parts by material, make sure the entire leaf is one material before you export out of Anim8or.
If it's lithunwrap then it looks like it doesn't seem very compatible with the file (or your mesh). You could try it in uvmapper classic or another program to see if you get the same results, and if it looks fine then export it from that program and import into lithunwrap and see if it helps.
If anything, attach your .an8 file so I can look at it in case it's a mesh error.