Step 1 Make the herbed oil: Place the garlic oil in the bowl of a food processor along with the basil, parsley, chile flakes and 1 1/4 teaspoons sea salt. Pulse to blend together, but do not fully puree; it is best left slightly coarse.
Step 2 Fill a pot large enough to accommodate the lobsters with cold water. Add enough sea salt to the water to approximate the salinity of the ocean. Add enough vinegar for the acidity to be noticeable but not strong. (You could also add herb stems, bay leaves and peppercorns, if you'd like.) Bring the water to a boil and add the lobsters.
Step 3Adjust the flame as needed to maintain a simmer, nothing more. Cook the lobsters for 3 minutes, then remove to an ice bath to stop the cooking. Drain the cooled lobsters.
Step 4Split the lobsters and remove the digestive tract and tomalley. If there is dark green roe in the lobster, make every effort to leave it undisturbed. Dab the flesh of the lobster with paper towels to dry.
Step 5Prepare the lobsters for the grill: Season the flesh of the lobsters lightly with sea salt and espelette, and brush the flesh with the herbed oil. Meanwhile, heat the grill to medium high.
Step 6Wipe down the grates with a touch of oil and allow it to burn off for several minutes. Place the lobsters, shell side down, for the first 2 to 3 minutes of cooking. Flip the lobsters, lightly brushing the shells with a touch of melted butter and sprinkling of sea salt. Cook the lobster, flesh side down, for 2 to 3 more minutes.
Step 7Remove the lobsters from the grill; the roe should have turned from green to red, and the flesh will be slightly caramelized. Brush the flesh with softened butter to make it glisten. Serve with lemon.