Bring a large pot of water to a boil and prepare an ice water bath. Add the lobster tails to the boiling water and cook until they curl up and the meat is white, about 8 minutes. Transfer them to the ice bath to stop the cooking process, about 2 minutes. Remove the meat from the shells, chop into small pieces and set aside.
In a large bowl, whisk together the mayonnaise, chives, tarragon, mustard, cayenne, shallot, lemon juice and some salt and pepper. Add the lobster meat, melted butter and 1 cup of the panko and mix to combine.
Put the remaining 1 cup panko on a baking sheet. Form the lobster mixture into appetizer-size cakes (about 1/4 cup each), coat the cakes in the panko and place on a plate or baking sheet.
Heat the olive oil in a large nonstick skillet over medium-high heat. Working in batches and adding oil as needed, fry the lobster cakes on each side until golden and cooked through, about 3 minutes per side. Serve topped with the Mango and Avocado Salsa.