I was thinking of the innards - specifically the white parts inside of the main body and what looks like eggs.
You can eat even shell. Ground shell is used in French Bisque to thicken the soup and make it more flavored.
I do like the claws and tail but the body is my big love. I adore picking it apart and finding that sweet meat as you break the body apart. It is tedious and only small amounts of meat but so good!!! I also like to take the roe and tomalie or lobster paste and put it with a bit of butter on a piece of fish and bake it, it then tastes like lobster!
Remove the Thorax shell (the saddle shaped one over the main body). Then you can take each leg off by gently wiggling and pulling. There's a nice piece of meat where the leg comes out of the body.
Then you suck the meat out of the leg.
The only parts that you need to avoid are the intestinal tract - the black line that runs through the tail, and the sac right behind the eyes which includes the brain, stomach, and other organs.
The tomalley is the edible yellow-green pasty substance which serves as the liver and pancreas. However, there are advisories in place by US federal and state agencies advising against eating the tomalley of Atlantic lobsters due to the high concentration of toxins present. I've eaten it before if that matters; it's delicious.
The roe present in female lobsters is also commonly eaten.
Anything else is edible, but not frequently eaten.