Prepare lobster: Place live lobster on its stomach and drive a sharp knife into point where tail meets head to kill lobster. Halve crosswise where tail meets chest cavity. Drain liquids from both halves into a small bowl, and spoon tomalley (and coral, if lobster is female) into another small bowl (tomalley is a dark gray-green mass in the head section or upper tail; coral will appear as dark red or black roe). Twist off claws close to lobster body, split again at elbow and crack each piece with a heavy knife. Discard head. Split tail in half, lengthwise, and remove brown intestinal vein. Halve each piece crosswise. You will have 8 pieces in all. Alternatively, lightly steam lobster and cool before cutting in 8 pieces.
In a large, heavy saucepan, heat oil over medium heat. Add onions and cook until wilted. Turn heat to high and add lobster pieces to saucepan as soon as they are ready. saute, shaking pan, 4 to 5 minutes until shells turn bright red. Push lobster to sides and add chicken breasts, skin side down. Cover and cook 5 to 6 minutes, until just cooked through. Using a slotted spoon, remove lobster and chicken pieces. When cool enough to handle, remove meat from lobster and chicken pieces and return shells and bones to saucepan. Meanwhile, deglaze pan with sherry and brandy, scraping bottom of pan to incorporate all browned bits. Add fish stock, white wine, reserved lobster liquids, chopped tomatoes and herbs; bring to a boil, partially cover and reduce heat to simmering.
Prepare the sauce: In a food processor, process nuts to a fine powder. Add reserved lobster tomalley (and coral), garlic, chocolate, sugar and saffron. Process until smooth. Strain lobster stock into a bowl and discard shells and bones. If desired, chill stock and remove any fat that accumulates on top; reheat before continuing. Transfer sauce to a saucepan and beat in hot stock, whisking well to combine. Simmer 15 minutes, stirring occasionally. For smoothest texture, strain soup again into cleaned saucepan and return to a simmer. Stir in arrowroot in a thin stream, whisking until soup thickens slightly. Slice reserved lobster and chicken meat, add to soup and warm for 5 minutes. Serve sprinkled with parsley.