Prepare the Live lobster by placing it on a stable cutting board; using a very sharp knife, split the lobster lengthwise from head to tail and remove the stomach sack and any green tomalley (or ask your fishmonger to do this). Pat the shells and meat dry with paper towels.
Preheat your grill to high or set your oven broiler to high and position the rack 6–8 inches from the heat source.
Brush the cut lobster flesh with Extra-virgin olive oil and season generously with Sea salt and freshly ground Black pepper; sprinkle a light pinch of Oregano over the meat for classic Mediterranean aromatics.
Make the sauce: warm 3–4 tablespoons of Extra-virgin olive oil in a small skillet over low heat, add minced Garlic and cook just until fragrant (about 30–45 seconds) without browning, then remove from heat and stir in Lemon juice, a pinch more Sea salt and a crack of Black pepper.
Place the lobster split-side up on the grill or a rimmed baking sheet if broiling; cook until the meat is opaque and just firm with a bit of char at the edges—about 8–12 minutes depending on size (larger lobsters may need a few extra minutes).
As soon as the lobster is cooked, spoon the warm garlic-lemon oil over the meat to coat and let rest for 1–2 minutes so the flavors meld.
Garnish with a generous scattering of chopped Flat-leaf parsley and serve with lemon wedges from the Lemon for squeezing at the table.
