Bring a large pot of water to a boil. Plunge the lobsters into the boiling water, cook for 8 minutes. Remove carefully and submerge in a bowl of ice water to immediately stop the cooking. Split the lobsters in half lengthwise and rinse out the head cavity and any veins that may be in the tail. Set aside.
Toss the papayas, mangos and tomatoes in a mixing bowl with the lime juice and cayenne and salt, to taste. Allow to sit for 10 minutes.
Meanwhile, preheat an outdoor grill to medium-high heat.
When ready to serve, brush a small amount of oil on the lobster meat and place the lobsters meat side down on the hot grill. Grill until lobster meat is lightly charred, about 4 minutes. Turn and cook the shell side until lobster is heated through, about 3 minutes more. Remove the lobster meat from the shell. Add the mint to salsa, mix, and put on serving plates. Serve the lobster meat on top of the salsa.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.