Boil a very large pot of water. Salt it and add the lobsters head first. Put the lid on the pot and boil until bright red and cooked, about 12 minutes. Drain and rinse under cold water.
While the lobster is cooking, peel the grapefruits to the quick, cutting first the top and bottom off, then cutting the skin off around them, removing all the pith. Cut the grapefruit sections with a knife into a large bowl, to catch the juice, and squeeze the remaining juice out of the membrane into the bowl as well.
To remove the lobster meat, twist off the claws. Use the back of a chef’s knife to crack both sides of the claws. Pull off the shell and reserve the meat. Use a pick to pull the meat out of the tube-like limbs attached to the claws. Now, twist the tails off the bodies. Lay them flat on its side and press down to crack the centre. Pull out the meat. Discard the bodies and shells, or use them to make lobster bisque.
Chop the lobster meat into large chunks for the salad and add it to the grapefruit. Cut the avocado and add it, along with a generous squeeze of lemon to keep its colour. Chop the green onions, including the green, and add along with the parsley leaves. Add the oil, salt, and pepper.
Toss. Taste, adjusting the seasonings (and adding a little lemon zest if you like), and serve.