To confuse you more, I'll propose other possible variations of the surname:
Juodakys (male), Juodakyte (unmarried female), Juodakiene (married woman);
Juodeikis, Juodeikyte, Juodeikiene;
and the one that you allready have: Juodikis, Juodikyte, Juodikiene.
Besides, the lithuanian word 'juodas' means 'black', 'akis' - 'eye', so the surname Juodakys should mean 'someone with black eyes'.
All these surnames are in lithuanian Phone book. I think, there is one more possible variation - Juodakis, but I didn't find it in the phone book (though it doesn't mean that there is no such surname at all).
Hope this helps. Good luck.