The Grand Cayman airport GCM is under extensive renovation and expansion right now and it is a pain in the neck, and interisland travel is very complicated. Hopefully things will get better when the construction is finished.
Try to book a direct flight from GC to LC on a Twin Otter, the LC airport is small and doesn't accept larger planes.
Some of the flights to LC stop on Brac and if you are on a larger plane (jet or turboprop) you will have to deplane, grab your luggage, and board a Twin Otter. It doesn't take much time but it is just one more delay on a long trip.
If you leave GC on a Twin Otter and it stops on Brac, you won't have to deplane and it will be a short stop.
When you first arrive on Grand Cayman you will have to go through customs and immigration and then check in for LC. It can take a long time to get through C&I if several other planes land around the same time.
After you exit C&I on GC, you roll your luggage cart out the door and immediately turn left to enter the airport ticket lobby. You then check your bags for LC and you will have to go through security to get to the departure lounge to board your flight to LC. There can be long lines to get through security especially on Saturday and Sunday and during the high season.
If you are in danger of missing your connection, tell one of the airport officers that you just arrived and are doing interisland transport to LC and may miss your flight - and he/she may try to assist you and move you forward - or not.
If you purchased any duty-free liquor (or other liquids/gels) at your local airport - you will NOT be able to take it through security (even if it is sealed and labeled as duty free) because it is greater than 3 oz., so wrap it well and put it in your checked bags before you re-check them. You cannot buy any duty-free liquor in the GCM departure lounge if you are traveling to another Cayman island.
On the trip home, the afternoon before you leave each person can pack a bag and have it sent ahead to GCM so that it will be waiting for you when you arrive. The hotel usually takes care of sending it to the airport, or if you are staying in a house or condo you can arrange to drop it off at the LC airport. This may help to make sure that all your luggage goes home with you, because the small planes coming from LC will have limited baggage space.
When you land on GC from LC they will try to herd you into the long incoming arrival line for Customs and Immigration with people who are just coming into the country, so get into the line for arriving locals and tell them they you just returned from LC and are connecting to your home flight.
The Immigration officer should waive you through so you can pick up your luggage (including the bag waiting for you) and head out the door. Tell the Customs agent that you are arriving from LC on your trip home and he/she should also waive you through. Go out the door, turn left, go into the ticket lobby and check in for your home flight(s).
You will then have to go through security and exit customs and immigration to get to the departure lounge to board your flight home.
If you find that you have a long interval time before boarding your homeward flight, you can check your bags and instead of going through security, jump on the free bus to the George Town Yacht Club that is just a few minutes away to relax, eat, drink, in a beautiful setting rather than sitting in the crowded, noisy departure lounge. But don't cut it too close, because the security lines can get long.
Hope this helps, have a great trip!