Unless - if JC is really holding a lituus - it is not the augural staff, but the trumpet ...

"Lydus (de Mens. iv.50) calls the lituus the sacerdotal trumpet, and says that it was employed by Romulus when he proclaimed the title of his city"

in this case it could fit, as JC was proclaimed parenti patriae and was seen as a new Romulus... who was also deified after his death.

Or maybe... on the coin he's not holding a lituus at all! :-)