Was your connecting flight from HNL to the mainland also on Hawaiian and booked on the same itinerary? If not, they're not obligated to accommodate you. If so, then either the new flight is still within the published minimum connect time and Hawaiian will be obligated to get you to your final destination one way or another, or it's not and the accommodations specialist will help change your flight.
That said, there are plenty of LIH to HNL flights so you should be able to switch to an earlier flight.
I'm not sure where else you would go. Nobody else flies from LIH to HNL. Are you hoping to get a nonstop flight from LIH to the mainland on another airline? Be sure to price that out before asking for a refund from Hawaiian...