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1
You need to par cook your lobster the old fashioned way, in a pot of boiling water, for about 10 minutes. Take it out of the water and let it cool until you can handle it easily. At that point, turn it on its back and using a really sharp knife, slice it right down the middle, lengthwise. (The tomalley will run all over, and since you don't grill that bit, if you like it, take a spoon to it at this juncture.) Take a meat mallet and give each claw a good whack so they crack slightly. Brush the exposed flesh with some chili oil and rub some more on the shell. Also brush the lemon slices with some chili oil. Set lobsters and lemons aside.
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2
Heat grill up to a high temperature.
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3
In a small pan, melt the butter, let it sit for a bit (still keeping it warm, though) and remove the clarified butter from the milk solids. You should have about 2-3 tablespoon of clarified butter. Into the butter put the lemon juice, minced thyme and salt and a squirt of hot sauce to taste. Set this aside as well, but keep it warm.
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4
When the grill is hot, place the lobster halves on it, exposed flesh down. Also put the lemon slices on the grill. The lobsters will only need 6-7 minutes on the grill and don't need to be turned. The lemon slices only need a couple of minutes one each side to get marked.
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5
When the lobster is done, work quickly to remove the tail, claw and leg meat and cut it all into bit sized pieces. Mix the meat with two tablespoons of the seasoned clarified butter mixture. You can mix in a bit more butter if you like, but remember that you just the meat dressed, not drowning. Gingerly mix in the avocado pieces. Serve the salad warm, with the grilled lemon slices and an extra sprig of thyme as garnish.
