I wouldn't do it.....There really isn't alot of time...given you should be checking back in 90 minutes ahead of the next flight.
LIH is a small airport, however depending on the number of flights going out at that same time..you could possibly run into a line-up at Security.
I don't believe renting a car during such a time frame would benefit you.
If... I could convince myself that this was worth doing.....the ONLY reason would be for a trip to Hamura's..... to have A bowl of soup and a whole Lilikoi Pie (To Go)! This experience alone would convince you to book your next trip to Kauai.