For the burnt lemon mayonnaise, place the lemon over an open flame and char the outside slowly for 10 minutes until very soft.
Place the lemon in a blender and mix until smooth. Add the mayonnaise and season to taste. Set aside.
Place the fennel in a bowl and add the olive oil and lemon juice. Season well and toss to coat.
Use a sharp knife to cut the lobster tails lengthwise. Remove the digestive tract and leave the meat in the shell.
Prepare a fire for medium coals or preheat a griddle pan. Brush the lobster with olive oil and place cut-side-down over the heat for 6 minutes. Turn and cook on the other side for 3-5 minutes. The shells should turn bright red.
Remove from the heat and serve immediately with the burnt lemon mayonnaise and fennel salad.