Pat lobster dry and set on a plate. Brush with 2 Tbsp. of the oil; season with salt and pepper. Refrigerate until needed.
Heat remaining oil in a medium pot set over medium heat. Add shallot and garlic and cook 2 minutes. Add rice and cook, stirring, until lightly toasted, about 3 minutes. Add wine and saffron. Bring to a gentle simmer, adjusting temperature as needed. Simmer wine until almost fully absorbed by the rice. Add 1 cup of stock. Stir and simmer until almost fully absorbed by rice. Add remaining stock, 1 cup at a time, stirring and simmering until it is almost fully absorbed before adding the next cup.
When rice is almost tender, preheat grill to medium-high. When the rice is tender, stir in peas, chopped parsley, Parmesan cheese, salt and pepper. Cover and reserve on low heat.
Lightly oil the grill. Grill the lobster, cut side down, 2 minutes.
Turn cut side up and grill 2 minutes more, or until cooked.
Divide risotto among 4 heated, shallow bowls. Set 3 half lobster tails in each bowl, garnish with lemon and parsley sprigs, and serve.
Note: Saffron threads are sold in bottles in the herb and spice aisle. Arborio rice is a short to medium grained rice, perfect for risotto. You can heat the stock in a pot set over medium-low heat. You may not need all of it to get the rice tender.