How to Make It
Plunge lobsters headfirst into boiling water, and boil 5 minutes. (Lobster will not be fully cooked.) Remove shell, and chop tail and claw meat into 1/2-inch pieces.
Combine lobster, lime juice, and lemon juice in a plastic or glass bowl. Cover and refrigerate 1 1/2 hours.
Brush fennel slices with 1/3 cup olive oil, and sprinkle with salt and pepper. Grill over medium-high heat 2 to 3 minutes on each side.
Combine remaining olive oil, lobster, fennel, red onion, and next 3 ingredients. Season to taste with salt and pepper. If mixture is too tart, add a pinch of sugar. Cover and refrigerate 30 minutes. Garnish, if desired.