I imagine that there are two people you would want to contact if you want official permission to compile such a dictionary. The first, obviously, is James Cameron, although I dunno how you could do that. The second, and much easier, I'd assume, to contact, would be Professor Paul Frommer, the linguist who developed the Na'vi language.
That being said, you won't be the first by far to contact Frommer about the Na'vi language, apparently, according to Wikipedia. Or the first to compile a dictionary of any sort.
http://en.wikipedia.org/wiki/Paul_Frommer
http://en.wikipedia.org/wiki/Na%27vi_language
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(No longer a mod)
On sabbatical...