I have been cooking lobster for so many years, using various techniques, including sous vides. When I go to most restaurants they ask, “grilled or boiled” and I use neither technique, so it is tough to decide. I discovered a long time ago, lobster is similar to chicken (but for different reasons) and you shouldn’t cook the tail and the claws, or body together. You have two choices, over cook, or under cook.
My technique is to first; kill the lobster by dividing the body in two; take a large sturdy knife and pierce the lobster at the topside of the cranial through to the underside. Then take a small pairing knife and carefully separate the body.
I then take a large enough copper pot and use some oil coating the surface of the pot. I heat the oil on high and then place the tail into the pot and cover it and shake it intermittently in order that it cooks evenly. It takes anywhere from 3/6 minutes or more depending on the size. The objective is to sear the lobster and cook it 80%. It should be slightly under cooked so you can cook in a final stage later on.
I often add it to a pasta but in this case I made it for a vegetable based dish and added back the claws and the body for flavor. The claws and the body have different physiology.
Lastly, when selecting a lobster, select the female or the male, as they are often better in taste.