In my opinion a 45 minute connection in LIH will be tight. Maybe Slippahs can confirm. LIH is not a big airport. Once you exit the plane, walking to the HA gate should really not be a factor. A 5 minute walk at the most regardless if AA is at one end of terminal and HA is at the other end.

Factors to consider for the 45 minute connection: flight is running late, your seat location on the plane (re; first class or coach in the rear of aircraft), just about everyone is on vacation and they have carry-ons which they have to remove from over head bins, passengers having no clue as to what is happening upon disembarking aircraft, etc. HA pretty much runs on time. That being said, unless they have alot of passengers coming over from your flight I really don't see them holding their aircraft. I don't know how you are going to buy your ticket but if you are running late, I am sure you would be put onto the next flight.

My question to you, what is your final destination? To be honest, there is no real reason to connect through LIH to your final destination. If you fly into LIH, more than likely you will grab your HA flight in LIH and fly into HNL and then onto your final destination. AA does fly into HNL, OGG and KOA. I would gather that you are flying out of the west coast if LIH is your final destination on an AA flight.